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 (C)</p> Signup and view all the answers

What is the result of adding two vectors?

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

Why is understanding vector addition important?

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

What can be used to illustrate vector addition graphically?

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

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

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

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

<p>Five steps forward (B)</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 (C)</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 (A)</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 (B)</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 (B)</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 (B)</p> Signup and view all the answers

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

<p>A vector with zero magnitude (A)</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 (D)</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 (A)</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 (C)</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 (D)</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 (B)</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 (D)</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 (A)</p> Signup and view all the answers

What is the difference between a positive and negative vector?

<p>Their directions are different (D)</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 (C)</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 (C)</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 (B)</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 (C)</p> Signup and view all the answers

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

<p>Zero (B)</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 (B)</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 (B)</p> Signup and view all the answers

What is the purpose of graphical techniques in vector addition?

<p>To visualize the addition of vectors (D)</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 (B)</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 (C)</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 (D)</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 (D)</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 (C)</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 (B)</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 (C)</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 (A)</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 (D)</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 (C)</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 (B)</p> Signup and view all the answers

What is the graphical representation of vector addition used for?

<p>To illustrate the addition of vectors (B)</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 (A)</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. (D)</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. (A)</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 (D)</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. (B)</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. (A)</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. (A)</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. (B)</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. (C)</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. (D)</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. (C)</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 (C)</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 (C)</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 (B)</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 (B)</p> Signup and view all the answers

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

<p>A vector with zero magnitude (C)</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 (C)</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 (B)</p> Signup and view all the answers

What is the graphical representation of vector addition used for?

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

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

<p>The resultant vector becomes zero (A)</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 (C)</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 (A)</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 (B)</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 (C)</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 (B)</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 (D)</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 (A)</p> Signup and view all the answers

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

<p>A vector with zero magnitude (A)</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 (C)</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 (B)</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 (C)</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 (D)</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 (D)</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 (D)</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 (B)</p> Signup and view all the answers

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

<p>The resultant vector is zero (A)</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 (B)</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 (B)</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 (D)</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 (D)</p> Signup and view all the answers

What does a negative vector represent?

<p>A vector with opposite direction to the reference positive direction (D)</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 (C)</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 (C)</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 (B)</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 (C)</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 (C)</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 (A)</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 (C)</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 (C)</p> Signup and view all the answers

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