Given that $\mathbf{a}$ and $\mathbf{b}$ are nonzero vectors such that $\|\mathbf{a} + \mathbf{b}\| = \|\mathbf{a} - \mathbf{b}\|,$ find the angle between $\mathbf{a}$ and $\mathbf{b},$ in degrees.
Question:
Given that $\mathbf{a}$ and $\mathbf{b}$ are nonzero vectors such that $\|\mathbf{a} + \mathbf{b}\| = \|\mathbf{a} - \mathbf{b}\|,$ find the angle between $\mathbf{a}$ and $\mathbf{b},$ in degrees.
Answer:
Let's think step by step.

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90^\circ
Given that $\mathbf{a}$ and $\mathbf{b}$ are nonzero vectors such that $\|\mathbf{a} + \mathbf{b}\| = \|\mathbf{a} - \mathbf{b}\|,$ find the angle between $\mathbf{a}$ and $\mathbf{b},$ in degrees.
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