Moderate

Cross product of two vectors is zero when they are:

Correct answer: C. Parallel to each other

  • A. Of different magnitude and perpendicular to each other
  • B. At an angle of 60°
  • C. Parallel to each other
  • D. At an angle of 90°

Explanation

The correct option is (c) - when two vectors are parallel to each other, their cross product will be zero. Now, let's go through each option and explain them: (a) Of different magnitude and perpendicular to each other: When two vectors are perpendicular to each other, their dot product is zero, not their cross product. The cross product measures the area of the parallelogram formed by the two vectors, so it won't be zero in this case. (b) At an angle of 60°: The cross product of two vectors is not necessarily zero when they are at an angle of 60°. The magnitude of the cross product depends on the magnitudes of the vectors and the sine of the angle between them. (c) Parallel to each other: When two vectors are parallel to each other, their cross product is indeed zero. This is because the cross product measures the perpendicular component between the vectors, and when they are parallel, there is no perpendicular component. (d) At an angle of 90°: When two vectors are at an angle of 90°, their cross product will have the maximum magnitude. It won't be zero in this case. In summary, when two vectors are parallel to each other, their cross product is zero.

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About Vectors and Equilibrium

Vectors have magnitude and direction, unlike scalars, and are combined by head-to-tail or parallelogram methods. Work covers rectangular components, equilibrium when the resultant force is zero, the scalar product for work and projections, and the vector product for torque and cross-product direction using the right-hand rule.

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