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. (C)</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. (B)</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 (C)</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 (D)</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 (A)</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 (C)</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 (A)</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 (C)</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 (D)</p> Signup and view all the answers

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

<p>A.B = 0 (C)</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) (B)</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 (D)</p> Signup and view all the answers

What is the magnitude of a zero vector?

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

What is the purpose of a unit vector?

<p>To give us the direction of a vector (A)</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 (D)</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 (A)</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 (D)</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 (A)</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 (B)</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 (A)</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 (B)</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 (C)</p> Signup and view all the answers

What is the condition for two vectors to be collinear?

<p>They have the same direction (A)</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 (D)</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 (A)</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 (B)</p> Signup and view all the answers

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