Gr 10 Physical Sciences Ch 15: Properties of vectors
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Questions and Answers

What are the two fundamental properties of vectors?

  • Direction and speed
  • Magnitude and direction (correct)
  • Magnitude and time
  • Time and speed

    • What determines if two vectors are equal?

  • Same magnitude and same direction (correct)
  • Same magnitude but different directions
  • Same direction but different magnitudes
  • Different magnitudes and different directions

    • What does a negative vector indicate?

  • A vector with infinite magnitude
  • A vector with zero magnitude
  • A vector with the same direction as the reference positive direction
  • A vector in the opposite direction to the reference positive direction (correct)

    • What is involved in adding vectors?

    <p>Both magnitude and direction are considered</p> Signup and view all the answers

    What is the result of adding two vectors?

    <p>A vector quantity</p> Signup and view all the answers

    Why is understanding vector addition important?

    <p>It is crucial for many applications in physics and engineering</p> Signup and view all the answers

    What can be used to illustrate vector addition graphically?

    <p>Displacement vectors</p> Signup and view all the answers

    What is an example of a situation where vector addition is used?

    <p>Moving a heavy box</p> Signup and view all the answers

    What is the result of adding two steps forward and three steps forward?

    <p>Five steps forward</p> Signup and view all the answers

    What is the process of subtracting a vector from another?

    <p>Adding a vector in the opposite direction</p> Signup and view all the answers

    What is the resultant vector in a vector addition problem?

    <p>The single vector that has the same effect as the combination of the individual vectors</p> Signup and view all the answers

    What is the definition of an equilibrant vector?

    <p>A vector with the same magnitude as the resultant vector but points in the opposite direction</p> Signup and view all the answers

    What is the head-to-tail method of vector addition?

    <p>A method that involves drawing accurate scale diagrams of the vectors</p> Signup and view all the answers

    What is the purpose of choosing a positive direction in vector addition?

    <p>To assign a direction to the resultant vector</p> Signup and view all the answers

    What is the result of adding a vector and its equilibrant?

    <p>A vector with zero magnitude</p> Signup and view all the answers

    What is the difference between vector addition and subtraction?

    <p>Vector addition involves adding vectors, while subtraction involves adding a vector in the opposite direction</p> Signup and view all the answers

    What is the purpose of graphical techniques in vector addition?

    <p>To visualize the vectors and their resultants</p> Signup and view all the answers

    What is the result of adding two vectors in opposite directions?

    <p>A vector with the difference of the magnitudes</p> Signup and view all the answers

    What is the condition for two vectors to be considered equal?

    <p>They have the same magnitude and direction</p> Signup and view all the answers

    What is the significance of the negative sign in a vector?

    <p>It indicates the direction opposite to the reference positive direction</p> Signup and view all the answers

    What is the result of adding two vectors with the same direction?

    <p>A vector with a larger magnitude</p> Signup and view all the answers

    What is the purpose of choosing a reference direction in vector addition?

    <p>To compare the directions of the vectors</p> Signup and view all the answers

    What is the difference between a positive and negative vector?

    <p>Their directions are different</p> Signup and view all the answers

    How do you represent a force of 30 N downward if the upward direction is defined as positive?

    <p>-30 N</p> Signup and view all the answers

    What is the significance of the graphical representation of vector addition?

    <p>To visualize the addition of vectors</p> Signup and view all the answers

    What is the importance of understanding vector addition in physics and engineering?

    <p>To solve many applications in physics and engineering</p> Signup and view all the answers

    What is the graphical representation of the equation 5 steps - 3 steps = 2 steps?

    <p>Moving 5 steps forward and then 3 steps backward</p> Signup and view all the answers

    What is the result of adding a vector and its equilibrant?

    <p>Zero</p> Signup and view all the answers

    What is the purpose of choosing a positive direction in vector addition?

    <p>To determine the direction of the resultant vector</p> Signup and view all the answers

    What is the difference between vector addition and subtraction?

    <p>Vector addition involves adding vectors, while vector subtraction involves adding a vector with its direction reversed</p> Signup and view all the answers

    What is the purpose of graphical techniques in vector addition?

    <p>To visualize the addition of vectors</p> Signup and view all the answers

    What is the definition of the resultant vector?

    <p>The single vector that has the same effect as the combination of individual vectors</p> Signup and view all the answers

    What is the result of adding two vectors in opposite directions?

    <p>A vector with a magnitude equal to the difference of the two vectors</p> Signup and view all the answers

    What is the process of subtracting a vector from another?

    <p>Adding the vector with its direction reversed</p> Signup and view all the answers

    What is the definition of the equilibrant vector?

    <p>The vector that has the same magnitude but opposite direction to the resultant vector</p> Signup and view all the answers

    What is the head-to-tail method of vector addition?

    <p>A method of adding vectors by drawing a diagram with the tail of the first vector attached to the head of the second vector</p> Signup and view all the answers

    What is the direction of a negative vector?

    <p>In the opposite direction to the reference positive direction</p> Signup and view all the answers

    What are the two fundamental properties of vectors that are compared to determine equality?

    <p>Magnitude and direction</p> Signup and view all the answers

    What is the result of adding two vectors with the same direction and magnitude?

    <p>A vector with the same direction and double the magnitude</p> Signup and view all the answers

    What is the purpose of defining a reference positive direction in vector addition?

    <p>To define a frame of reference for vector addition</p> Signup and view all the answers

    How do you represent a force of 20 N downward if the upward direction is defined as positive?

    <p>F = -20 N</p> Signup and view all the answers

    What is the result of adding two vectors that are perpendicular to each other?

    <p>A vector with a direction perpendicular to the original vectors</p> Signup and view all the answers

    What is the graphical representation of vector addition used for?

    <p>To illustrate the addition of vectors</p> Signup and view all the answers

    What is the importance of understanding vector addition in physics and engineering?

    <p>It is crucial for many applications in physics and engineering</p> Signup and view all the answers

    When adding vectors graphically, what is the correct order of drawing the vectors?

    <p>Draw the first vector, then the second vector, and finally the resultant vector.</p> Signup and view all the answers

    What is the relationship between the resultant vector and the equilibrant vector?

    <p>The resultant vector has the same magnitude as the equilibrant vector but opposite direction.</p> Signup and view all the answers

    If you pull a box with a force of 20 N to the right and your friend pulls it with a force of 15 N to the left, what is the total force?

    <p>5 N to the left</p> Signup and view all the answers

    What is the purpose of choosing a reference direction in vector addition?

    <p>To define the positive direction.</p> Signup and view all the answers

    When subtracting a vector from another, what is the correct approach?

    <p>Add the first vector to the negative of the second vector.</p> Signup and view all the answers

    What is the graphically represented by the equation 2 steps + 3 steps = 5 steps?

    <p>The addition of two vectors in the same direction.</p> Signup and view all the answers

    Why is the order of addition of vectors not important?

    <p>Because the resultant vector is always the same regardless of the order of addition.</p> Signup and view all the answers

    What is the purpose of the head-to-tail method in vector addition?

    <p>To add vectors graphically.</p> Signup and view all the answers

    What is the result of adding two vectors with the same magnitude but opposite directions?

    <p>A resultant vector with zero magnitude.</p> Signup and view all the answers

    What is the significance of the negative sign in a vector?

    <p>It indicates the vector is in the opposite direction.</p> Signup and view all the answers

    What is the consequence of changing the direction of a negative vector?

    <p>It becomes a positive vector</p> Signup and view all the answers

    If two vectors have the same magnitude but opposite directions, what is their sum?

    <p>A vector with zero magnitude</p> Signup and view all the answers

    What is the purpose of defining a reference positive direction in vector addition?

    <p>To establish a common direction for comparison</p> Signup and view all the answers

    If two vectors are equal, what can be said about their magnitudes and directions?

    <p>They have the same magnitude and the same direction</p> Signup and view all the answers

    What is the result of adding a vector to its negative?

    <p>A vector with zero magnitude</p> Signup and view all the answers

    What is the significance of the negative sign in a vector?

    <p>It indicates the opposite direction to the reference positive direction</p> Signup and view all the answers

    What is the importance of understanding vector addition in physics and engineering?

    <p>It is crucial for many applications in physics and engineering</p> Signup and view all the answers

    What is the graphical representation of vector addition used for?

    <p>To illustrate vector addition graphically</p> Signup and view all the answers

    What is the effect of adding a vector and its equilibrant?

    <p>The resultant vector becomes zero</p> Signup and view all the answers

    What is the purpose of choosing a positive direction in vector addition?

    <p>To distinguish between positive and negative vectors</p> Signup and view all the answers

    What is the graphical representation of the equation 5 steps - 3 steps = 2 steps?

    <p>A vector 5 steps long subtracted by a vector 3 steps long</p> Signup and view all the answers

    What is the relationship between the resultant vector and the equilibrant vector?

    <p>The equilibrant vector has the same magnitude but opposite direction as the resultant vector</p> Signup and view all the answers

    What is the purpose of defining a reference positive direction in vector addition?

    <p>To distinguish between positive and negative vectors</p> Signup and view all the answers

    What is the correct approach when subtracting a vector from another?

    <p>Add the two vectors with the direction of the second vector reversed</p> Signup and view all the answers

    What is the result of adding two vectors that are perpendicular to each other?

    <p>A vector with a magnitude greater than the original vectors</p> Signup and view all the answers

    What is the purpose of graphical techniques in vector addition?

    <p>To visualize and understand the addition of vectors</p> Signup and view all the answers

    What is the result of adding a vector and its negative?

    <p>A vector with zero magnitude</p> Signup and view all the answers

    What is the head-to-tail method of vector addition?

    <p>A graphical method of adding vectors by drawing them head to tail</p> Signup and view all the answers

    If two vectors (\vec{A}) and (\vec{B}) have the same magnitude but opposite directions, what is the value of (\vec{A} + \vec{B})?

    <p>0</p> Signup and view all the answers

    A vector (\vec{F}) has a magnitude of 10 N and points in the upward direction. If the upward direction is defined as positive, what is the representation of a vector (\vec{G}) that has the same magnitude but points in the downward direction?

    <p>(\vec{G} = -10) N</p> Signup and view all the answers

    If two vectors are added in opposite directions, what is the resultant vector?

    <p>The difference between the magnitudes of the two vectors</p> Signup and view all the answers

    When adding vectors graphically, what is the correct approach to ensure that the resultant vector is accurate?

    <p>Draw the vectors head-to-tail and then add them</p> Signup and view all the answers

    What is the purpose of the head-to-tail method in vector addition?

    <p>To visualize the individual vectors and their resultant vector</p> Signup and view all the answers

    If two vectors (\vec{A}) and (\vec{B}) are added together, and the resultant vector is equal to zero, what can be concluded about the two vectors?

    <p>They are equal in magnitude and opposite in direction</p> Signup and view all the answers

    What is the effect of adding a vector and its equilibrant?

    <p>The resultant vector is zero</p> Signup and view all the answers

    What is the purpose of defining a reference positive direction in vector addition?

    <p>To provide a standard direction for adding vectors</p> Signup and view all the answers

    What is the significance of choosing a reference direction in vector addition?

    <p>To define a positive direction for the vectors</p> Signup and view all the answers

    What is the difference between vector addition and subtraction?

    <p>Vector addition involves adding vectors, while subtraction involves adding the negative of a vector</p> Signup and view all the answers

    What is necessary for two vectors to be considered equal?

    <p>They have the same magnitude and direction</p> Signup and view all the answers

    What does a negative vector represent?

    <p>A vector with opposite direction to the reference positive direction</p> Signup and view all the answers

    What is the result of adding two vectors with the same direction and magnitude?

    <p>A vector with double the magnitude</p> Signup and view all the answers

    What is the purpose of choosing a reference positive direction in vector addition?

    <p>To establish a common direction for all vectors</p> Signup and view all the answers

    What is the significance of the graphical representation of vector addition?

    <p>It illustrates the mathematical concept of vector addition</p> Signup and view all the answers

    What is the result of subtracting a vector from another?

    <p>Adding a vector in the opposite direction</p> Signup and view all the answers

    What is the purpose of graphical techniques in vector addition?

    <p>To illustrate the direction of the resultant vector</p> Signup and view all the answers

    What is the definition of the resultant vector?

    <p>The single vector that has the same effect as the combination of individual vectors</p> Signup and view all the answers

    What is the relationship between the resultant vector and the equilibrant vector?

    <p>The resultant vector and the equilibrant vector have the same magnitude but opposite direction</p> Signup and view all the answers

    What is the head-to-tail method of vector addition?

    <p>A method of adding vectors by drawing them from head to tail</p> Signup and view all the answers

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