Let a, b be non-zero, perpendicular, | a|=| b|, and | a b|=| a|.

Question

Accepted Answer

$|\vec a||\vec b|\sin90^{\circ} = |\vec a| \Rightarrow |\vec b|=1=|\vec a|$, so $\vec a,\vec b,\vec a\times\vec b$ are mutually perpendicular unit vectors. Take $\vec a=\hat i,\vec b=\hat j$, so $\vec a\times\vec b=\hat k$.

$$\vec a+\vec b+\vec a\times\vec b = \hat i+\hat j+\hat k$$
$$\cos\theta = \frac{(\hat i+\hat j+\hat k)\cdot\hat i}{\sqrt3\cdot1} = \frac1{\sqrt3} \implies \theta=\cos^{-1}\frac1{\sqrt3}$$

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