Question

If $\mathbf{v}·\mathbf{w}=0$, then the two vectorsvandw are ____.

Short answer

If $\mathbf{v}·\mathbf{w}=0$, then the two vectors vandw are orthogonal.

Step-by-step solution

Step 1. Given Information  

We are given an incomplete statement about the dot product.

We have to complete the given statement

Step 2. Completing the Statement 

The dot product is given by,

$\mathbf{v}·\mathbf{w}=vw\cos \theta$

If role="math" localid="1646828138762" $\mathbf{v}·\mathbf{w}=0$, then

$$\begin{gathered} vw\cos \theta =0 \\ \cos \theta =0 \\ \theta =\frac{\pi }{2} \end{gathered}$$

That means the vectors are orthogonal.