Find |vec{a} times vec{b}|, if vec{a}=hat{i}- | vedclass

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(A) We have,$\vec{a} = \hat{i} - 7\hat{j} + 7\hat{k}$ and $\vec{b} = 3\hat{i} - 2\hat{j} + 2\hat{k}$.The cross product $\vec{a} 	imes \vec{b}$ is giv

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$19\sqrt{2}$

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(A) We have,$\vec{a} = \hat{i} - 7\hat{j} + 7\hat{k}$ and $\vec{b} = 3\hat{i} - 2\hat{j} + 2\hat{k}$.The cross product $\vec{a} 	imes \vec{b}$ is given by the determinant:$\vec{a} 	imes \vec{b} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & -7 & 7 \ 3 & -2 & 2 \end{vmatrix}$Expanding the determinant:$= \hat{i}((-7)(2) - (7)(-2)) - \hat{j}((1)(2) - (7)(3)) + \hat{k}((1)(-2) - (-7)(3))$$= \hat{i}(-14 + 14) - \hat{j}(2 - 21) + \hat{k}(-2 + 21)$$= 0\hat{i} + 19\hat{j} + 19\hat{k}$Now,find the magnitude $|\vec{a} 	imes \vec{b}| = \sqrt{0^2 + 19^2 + 19^2}$$= \sqrt{19^2 + 19^2} = \sqrt{2 	imes 19^2} = 19\sqrt{2}$.

Find $|\vec{a} \times \vec{b}|,$ if $\vec{a}=\hat{i}-7 \hat{j}+7 \hat{k}$ and $\vec{b}=3 \hat{i}-2 \hat{j}+2 \hat{k}.$

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