If the dot product of two nonzero vectors A and B is zero then the magnitude of their cross product is _.
Correct answer: C. AB
- A. 0
- B. 1
- C. AB
- D. -AB
Explanation
If the dot product of two nonzero vectors (A) and (B) is zero, it means that they are orthogonal (perpendicular) to each other. In this case, the magnitude of their cross product is equal to the product of their magnitudes multiplied by the sine of the angle between them. Since the sine of 90 degrees is 1, when (A) and (B) are orthogonal, the magnitude of their cross product simplifies to AB. Therefore, option c is correct.
This question appeared on the KMU Centralized Admission Test 2022 paper, which you can sit online with every answer explained.
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About Vector Product
The vector product, or cross product, gives a vector perpendicular to two multiplying vectors, with magnitude AB sin θ and direction set by the right-hand rule. It covers properties such as anti-commutation, area from cross products, torque and angular momentum. Unlike the dot product, its result is a vector.
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