If $\|\mathbf{a}\| = 3$ and $\|\mathbf{b}\| = 4,$ then find all $k$ for which the vectors $\mathbf{a} + k \mathbf{b}$ and $\mathbf{a} - k \mathbf{b}$ are orthogonal.
Question:
If $\|\mathbf{a}\| = 3$ and $\|\mathbf{b}\| = 4,$ then find all $k$ for which the vectors $\mathbf{a} + k \mathbf{b}$ and $\mathbf{a} - k \mathbf{b}$ are orthogonal.
Answer:
Let's think step by step.

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\frac{3}{4}, -\frac{3}{4}
If $\|\mathbf{a}\| = 3$ and $\|\mathbf{b}\| = 4,$ then find all $k$ for which the vectors $\mathbf{a} + k \mathbf{b}$ and $\mathbf{a} - k \mathbf{b}$ are orthogonal.
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