If the dot product of two nonzero vectors is zero,the vectors must be perpendicular to each other.

Question

Quizplus · Accepted Answer

The dot product of two vectors is given by the formula:

a · b = |a| |b| cos(theta)

where a and b are the vectors, |a| and |b| are their magnitudes, and theta is the angle between them.

If the dot product of two nonzero vectors is zero, then cos(theta) must be zero. The only way for cos(theta) to be zero is if theta is equal to 90 degrees (or pi/2 radians). This means that the two vectors are perpendicular to each other, since the angle between perpendicular vectors is always 90 degrees. Therefore, the statement is true: if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other.

If the Dot Product of Two Nonzero Vectors Is Zero,the