Chapter 6, Problem 1FTD

If the scalar product of two nonzero vectors is zero, what can you conclude about their relative directions?

To determine

To explain: the relative directions of the scalar products of two nonzero vectors.

Explanation of Solution

Given information:

The scalar product of a and b is 0

Calculation:

The scalar product of a and b is as follows:

$a\cdot b=\left|a\right|\left|b\right|\cos \theta$

Substitute 0 for $a\cdot b$

$\begin{array}{l}0=\left|a\right|\left|b\right|\cos \theta \\ \cos \theta =0\\ \theta ={\cos }^{-1}\left(0\right)\\ \theta =90°\end{array}$

Therefore, the relative directions of the scalar products of two nonzero vectors are perpendicular or orthogonal.