Vectors
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Questions and Answers

What is the condition for two vectors A and B to be anti-parallel?

  • One vector is a scalar multiple of another.
  • Both have opposite directions. (correct)
  • Both have the same direction.
  • One vector is a scalar non-zero positive multiple of another.

    • What is the resultant vector in the triangle law of vector addition?

  • The difference of the two vectors.
  • The sum of the two vectors.
  • The diagonal of the triangle.
  • The closing side of the triangle in the opposite order. (correct)

    • What is the axis of rotation for an axial vector?

  • The direction of the unit vector.
  • The direction of the zero vector.
  • The direction of the vector.
  • The direction perpendicular to the vector. (correct)

    • What is the unit vector of a vector A?

    <p>A vector divided by its magnitude.</p> Signup and view all the answers

    What is the condition for three or more vectors to be coplanar?

    <p>They lie in the same plane.</p> Signup and view all the answers

    What is the primary condition for a physical quantity to be considered a vector?

    <p>Obeying the laws of vector algebra</p> Signup and view all the answers

    What is the term for vectors that have a starting point or point of application?

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

    What is the direction of the axis of rotation for axial vectors?

    <p>Along the axis of rotation</p> Signup and view all the answers

    What is the purpose of the right-hand rule in vector algebra?

    <p>To define the orientation of a coordinate system</p> Signup and view all the answers

    Which of the following is NOT a characteristic of equal vectors?

    <p>Obeying the laws of vector algebra</p> Signup and view all the answers

    If the angle between vectors A and B is 0°, what is the value of R?

    <p>R = A + B</p> Signup and view all the answers

    If A and B are two vectors with an angle θ between them, what is the formula for their scalar product?

    <p>A.B = AB cosθ</p> Signup and view all the answers

    What is the condition for vectors A and B to be perpendicular?

    <p>A.B = 0</p> Signup and view all the answers

    What is the resultant vector R of two vectors A and B when θ = 90°?

    <p>R = √(A² + B²)</p> Signup and view all the answers

    What is the resolution of a vector R into its rectangular components Rx, Ry, and Rz?

    <p>Rx = R cosθ, Ry = R sinθ, Rz = 0</p> Signup and view all the answers

    What is the magnitude of a zero vector?

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

    Which of the following is a necessary condition for three vectors to be coplanar?

    <p>They must lie in the same plane</p> Signup and view all the answers

    What is the purpose of a unit vector?

    <p>To give us the direction of a vector</p> Signup and view all the answers

    What is the result of adding two vectors A and B using the triangle law of vector addition?

    <p>A vector with magnitude equal to the closing side of the triangle</p> Signup and view all the answers

    What is the characteristic of two vectors that are collinear?

    <p>They have the same support or axis</p> Signup and view all the answers

    What is the condition for the resultant of two vectors A and B to be zero?

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

    Which of the following is a characteristic of coplanar vectors?

    <p>They can be represented by the sides of a polygon</p> Signup and view all the answers

    What is the direction of the z-axis in a Right-Handed Triad?

    <p>Perpendicular to the x-y plane</p> Signup and view all the answers

    What is the purpose of a unit vector?

    <p>To have a vector with a magnitude of one unit</p> Signup and view all the answers

    What is true about the magnitudes of collinear vectors A and B?

    <p>Their magnitudes can be in any ratio</p> Signup and view all the answers

    What is the key concept in the parallelogram law of vector addition?

    <p>The diagonal of the parallelogram represents the resultant</p> Signup and view all the answers

    What is the condition for two vectors to be collinear?

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

    What is the condition for vector addition using the triangle law of vector addition?

    <p>The vectors must be coplanar</p> Signup and view all the answers

    What is the characteristic of the unit vectors î, ĵ, and k̂?

    <p>They have a magnitude of 1 unit</p> Signup and view all the answers

    What is the condition for two vectors to be coplanar?

    <p>They must lie in the same plane</p> Signup and view all the answers

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