If bar{a} = 4hat{i} + 3hat{j} + hat{k} and ba | vedclass

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(B) First,calculate $|\bar{a}|^2 = 4^2 + 3^2 + 1^2 = 16 + 9 + 1 = 26$. Also,$\bar{a} \cdot \bar{b} = (4)(1) + (3)(-2) + (1)(2) = 4 - 6 + 2 = 0$. Using

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$676 \bar{b}$

Vedclass · Answer

(B) First,calculate $|\bar{a}|^2 = 4^2 + 3^2 + 1^2 = 16 + 9 + 1 = 26$. Also,$\bar{a} \cdot \bar{b} = (4)(1) + (3)(-2) + (1)(2) = 4 - 6 + 2 = 0$. Using the vector triple product formula $\bar{a} 	imes (\bar{a} 	imes \bar{b}) = (\bar{a} \cdot \bar{b})\bar{a} - (\bar{a} \cdot \bar{a})\bar{b}$,since $\bar{a} \cdot \bar{b} = 0$,we have $\bar{a} 	imes (\bar{a} 	imes \bar{b}) = -|\bar{a}|^2 \bar{b} = -26\bar{b}$. Now,let $\bar{v} = \bar{a} 	imes (\bar{a} 	imes \bar{b}) = -26\bar{b}$. Then $\bar{a} 	imes (\bar{a} 	imes \bar{v}) = \bar{a} 	imes (\bar{a} 	imes (-26\bar{b})) = -26(\bar{a} 	imes (\bar{a} 	imes \bar{b}))$. Substituting the previous result: $-26(-26\bar{b}) = 676\bar{b}$. Thus,the correct option is $B$.

If $\bar{a} = 4\hat{i} + 3\hat{j} + \hat{k}$ and $\bar{b} = \hat{i} - 2\hat{j} + 2\hat{k}$,then find the value of $\bar{a} \times (\bar{a} \times (\bar{a} \times (\bar{a} \times \bar{b})))$.

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