Let a, b and c be three unit vectors such that a( b c)=√32( b+ c).

Question

Let $\vec a,\vec b$ and $\vec c$ be three unit vectors such that $\vec a	imes(\vec b	imes\vec c)=\dfrac{\sqrt3}2(\vec b+\vec c)$. If $\vec b$ is not parallel to $\vec c$, then the angle between $\vec a$ and $\vec b$ is:

Accepted Answer

$$\vec a\times(\vec b\times\vec c) = (\vec a\cdot\vec c)\vec b-(\vec a\cdot\vec b)\vec c = \frac{\sqrt3}2\vec b+\frac{\sqrt3}2\vec c$$

Comparing coefficients: $\vec a\cdot\vec b=-\dfrac{\sqrt3}2$ (unit vectors), so $\cos\theta=-\dfrac{\sqrt3}2 \implies \theta=\dfrac{5\pi}6$.

Solutions · 1