If |vec{a}|=3,then the value of |vec{a} times | vedclass

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(C) Let $\vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}$.Given that $|\vec{a}| = 3$,we have $a_1^2 + a_2^2 + a_3^2 = 3^2 = 9$.Now,$\vec{a} 	imes \

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$18$

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(C) Let $\vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}$.Given that $|\vec{a}| = 3$,we have $a_1^2 + a_2^2 + a_3^2 = 3^2 = 9$.Now,$\vec{a} 	imes \hat{i} = (a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}) 	imes \hat{i} = -a_2 \hat{k} + a_3 \hat{j}$.So,$|\vec{a} 	imes \hat{i}|^2 = a_2^2 + a_3^2$.Similarly,$|\vec{a} 	imes \hat{j}|^2 = a_1^2 + a_3^2$ and $|\vec{a} 	imes \hat{k}|^2 = a_1^2 + a_2^2$.Adding these,we get $|\vec{a} 	imes \hat{i}|^2 + |\vec{a} 	imes \hat{j}|^2 + |\vec{a} 	imes \hat{k}|^2 = (a_2^2 + a_3^2) + (a_1^2 + a_3^2) + (a_1^2 + a_2^2) = 2(a_1^2 + a_2^2 + a_3^2)$.Substituting the value,$2(9) = 18$.

If $|\vec{a}|=3$,then the value of $|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2$ is . . . . . . .

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