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## Q. 2.4

Show that the vectors u = 3i – 4j and v = 4i + 3j are orthogonal.

## Verified Solution

$\mathbf{u} \cdot \mathbf{v}=3 \cdot 4-4 \cdot 3=0$. This implies that $\cos \varphi=(\mathbf{u} \cdot \mathbf{v}) /(|\mathbf{u} \| \mathbf{v}|)=0$. Since $\varphi$ is in the interval $[0, \pi], \varphi=\pi / 2$.