Let \vec{a} \vec{b} (\vec{a}\times\vec{b}) be unit vectors. What is (\vec{a}\cdot\vec{b}) equal to?

Explanation

We are given that |\vec{a}| = 1, |\vec{b}| = 1, and |\vec{a}\times\vec{b}| = 1. The magnitude of the cross product is |\vec{a}||\vec{b}|\sin\theta = 1 \implies 1 \cdot 1 \cdot \sin\theta = 1 \implies \theta = 90^{\circ}. Thus, the dot product \vec{a}\cdot\vec{b} = |\vec{a}||\vec{b}|\cos 90^{\circ} = 0.

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