Question
Find the angle $\theta$ between the vectors.$$\begin{aligned}&\mathbf{u}=\langle 1,1,1\rangle \\&\mathbf{v}=\langle 2,1,-1\rangle\end{aligned}$$
Step 1
The dot product is calculated as follows: $$ \mathbf{u} \cdot \mathbf{v} = u_1v_1 + u_2v_2 + u_3v_3 $$ Substituting the given values, we get: $$ \mathbf{u} \cdot \mathbf{v} = (1)(2) + (1)(1) + (1)(-1) = 2 $$ Show more…
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