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If $\mathbf{a}=\mathbf{i}+2 \mathbf{j}-3 \mathbf{k}$ and $\mathbf{b}=3 \mathbf{i}-\mathbf{j}+2 \mathbf{k}$, then the angle between the vectors $\mathbf{a}+\mathbf{b}$ and $\mathbf{a}-\mathbf{b}$ is
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The correct answer is:
$90^{\circ}$
We have $\mathbf{a + b = 4 i + j - \mathbf { k }}$ and $\mathbf{a - b}=-2 \mathbf{i}+3 \mathbf{j}-5 \mathbf{k}$.
Clearly $(\mathbf{a}+\mathbf{b}) .(\mathbf{a}-\mathbf{b})=0 . \quad$ Hence $(\mathbf{a}+\mathbf{b}) \perp(\mathbf{a}-\mathbf{b})$.
Clearly $(\mathbf{a}+\mathbf{b}) .(\mathbf{a}-\mathbf{b})=0 . \quad$ Hence $(\mathbf{a}+\mathbf{b}) \perp(\mathbf{a}-\mathbf{b})$.
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