|vec{a} times hat{i}|^2 + |vec{a} times hat{j | vedclass

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(B) Let $\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}$.Then,$|\vec{a}|^2 = a_1^2 + a_2^2 + a_3^2$.Now,$\vec{a} 	imes \hat{i} = (a_1\hat{i} + a_2\ha

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$2|\vec{a}|^2$

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(B) Let $\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}$.Then,$|\vec{a}|^2 = a_1^2 + a_2^2 + a_3^2$.Now,$\vec{a} 	imes \hat{i} = (a_1\hat{i} + a_2\hat{j} + a_3\hat{k}) 	imes \hat{i} = a_1(\hat{i} 	imes \hat{i}) + a_2(\hat{j} 	imes \hat{i}) + a_3(\hat{k} 	imes \hat{i}) = 0 - a_2\hat{k} + a_3\hat{j}$.So,$|\vec{a} 	imes \hat{i}|^2 = |a_3\hat{j} - a_2\hat{k}|^2 = a_3^2 + a_2^2$.Similarly,$|\vec{a} 	imes \hat{j}|^2 = |a_1\hat{k} - a_3\hat{i}|^2 = a_1^2 + a_3^2$.And,$|\vec{a} 	imes \hat{k}|^2 = |a_2\hat{i} - a_1\hat{j}|^2 = a_2^2 + a_1^2$.Adding these three,we get:$|\vec{a} 	imes \hat{i}|^2 + |\vec{a} 	imes \hat{j}|^2 + |\vec{a} 	imes \hat{k}|^2 = (a_3^2 + a_2^2) + (a_1^2 + a_3^2) + (a_2^2 + a_1^2) = 2(a_1^2 + a_2^2 + a_3^2) = 2|\vec{a}|^2$.

$|\vec{a} \times \hat{i}|^2 + |\vec{a} \times \hat{j}|^2 + |\vec{a} \times \hat{k}|^2 = $

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