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(A) Using the vector triple product identity,we have $\overline{a} 	imes (\overline{b} 	imes \overline{c}) = (\overline{a} \cdot \overline{c}) \over

Vedclass · Accepted Answer

$\frac{5 \pi}{6}$

Vedclass · Answer

(A) Using the vector triple product identity,we have $\overline{a} 	imes (\overline{b} 	imes \overline{c}) = (\overline{a} \cdot \overline{c}) \overline{b} - (\overline{a} \cdot \overline{b}) \overline{c}$.Given $\overline{a} 	imes (\overline{b} 	imes \overline{c}) = \frac{\sqrt{3}}{2} \overline{b} + \frac{\sqrt{3}}{2} \overline{c}$,we compare the coefficients of $\overline{b}$ and $\overline{c}$ since $\overline{b}$ and $\overline{c}$ are not parallel.Thus,$\overline{a} \cdot \overline{c} = \frac{\sqrt{3}}{2}$ and $-\overline{a} \cdot \overline{b} = \frac{\sqrt{3}}{2}$,which implies $\overline{a} \cdot \overline{b} = -\frac{\sqrt{3}}{2}$.Since $\overline{a}$ and $\overline{b}$ are unit vectors,$\overline{a} \cdot \overline{b} = |\overline{a}| |\overline{b}| \cos 	heta = (1)(1) \cos 	heta = \cos 	heta$.Therefore,$\cos 	heta = -\frac{\sqrt{3}}{2}$.Since $	heta \in [0, \pi]$,we have $	heta = \frac{5\pi}{6}$.

Let $\overline{a}, \overline{b}$ and $\overline{c}$ be three unit vectors such that $\overline{a} \times(\overline{b} \times \overline{c})=\frac{\sqrt{3}}{2}(\overline{b}+\overline{c})$. If $\overline{b}$ is not parallel to $\overline{c}$,then the angle between $\overline{a}$ and $\overline{b}$ is

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