If bar{a}, bar{b}, bar{c} are non-coplanar un | vedclass

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(D) Using the vector triple product formula,$\bar{a} 	imes (\bar{b} 	imes \bar{c}) = (\bar{a} \cdot \bar{c})\bar{b} - (\bar{a} \cdot \bar{b})\bar{c}

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$\frac{3\pi}{4}$

Vedclass · Answer

(D) Using the vector triple product formula,$\bar{a} 	imes (\bar{b} 	imes \bar{c}) = (\bar{a} \cdot \bar{c})\bar{b} - (\bar{a} \cdot \bar{b})\bar{c}$.Given $\bar{a} 	imes (\bar{b} 	imes \bar{c}) = \frac{1}{\sqrt{2}}\bar{b} + \frac{1}{\sqrt{2}}\bar{c}$.Comparing the coefficients of $\bar{b}$ and $\bar{c}$ (since $\bar{b}$ and $\bar{c}$ are non-coplanar,they are linearly independent),we get:$\bar{a} \cdot \bar{c} = \frac{1}{\sqrt{2}}$ and $-(\bar{a} \cdot \bar{b}) = \frac{1}{\sqrt{2}}$,which implies $\bar{a} \cdot \bar{b} = -\frac{1}{\sqrt{2}}$.Since $\bar{a}$ and $\bar{b}$ are unit vectors,$\bar{a} \cdot \bar{b} = |\bar{a}||\bar{b}| \cos 	heta = \cos 	heta$.Thus,$\cos 	heta = -\frac{1}{\sqrt{2}}$.Therefore,$	heta = \frac{3\pi}{4}$.

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