If the dot product of two non-zero vectors A and B is zero, their cross product will be of magnitude:

Explanation

If the dot product of two non-zero vectors A and B is zero, their cross product will indeed be of magnitude AB. The dot product of two vectors A and B is given by the formula A · B = |A| |B| cos θ, where |A| represents the magnitude of vector A, |B| represents the magnitude of vector B, and θ represents the angle between vectors A and B. If the dot product of A and B is zero, it means that A · B = 0. Rearranging the formula, we get |A| |B| cos θ = 0. Now, let's consider the cross product of A and B, denoted as A x B. The magnitude of the cross product is given by |A x B| = |A| |B| sin θ, where sin θ represents the sine of the angle between vectors A and B. Since the dot product of A and B is zero, we can conclude that cos θ = 0. This implies that the angle θ between A and B is 90°, making them perpendicular to each other. In this case, sin θ = 1, because the sine of 90° is 1. Therefore, |A x B| = |A| |B| sin θ = |A| |B| * 1 = |A| |B| = AB. So, if the dot product of two non-zero vectors A and B is zero, their cross product will be of magnitude AB.