Find the angle between two vectors p and q, if |p x q| = p.q
2026-03-29 18:32:37.1774809157
Find the angle between two vectors p and q, if |p x q| = p.q
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I am assuming that $\mathbf{p},\mathbf{q}\neq0$. Let $\theta$ be the angle between $\mathbf{p}$ and $\mathbf{q}$.
Since $\|\mathbf{p}\times\mathbf{q}\|=\|\mathbf{p}\|.\|\mathbf{q}\|.\sin\theta$ and $\mathbf{p}.\mathbf{q}=\|\mathbf p\|.\|\mathbf q\|.\cos\theta$, the angle is such that $\sin\theta=\cos\theta$. Since $\theta\in[0,\pi]$, the only possible value of $\theta$ is $\frac\pi4$.