If overrightarrow A = 3hat i + hat j + 2hat k | vedclass

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Question

(B) The cross product $\overrightarrow A 	imes \overrightarrow B$ is calculated using the determinant method:$\overrightarrow A 	imes \overrightarro

Vedclass · Accepted Answer

$8\sqrt 3 $

Vedclass · Answer

(B) The cross product $\overrightarrow A 	imes \overrightarrow B$ is calculated using the determinant method:$\overrightarrow A 	imes \overrightarrow B = \begin{vmatrix} \hat i & \hat j & \hat k \ 3 & 1 & 2 \ 2 & -2 & 4 \end{vmatrix}$$= \hat i(1 	imes 4 - 2 	imes -2) - \hat j(3 	imes 4 - 2 	imes 2) + \hat k(3 	imes -2 - 1 	imes 2)$$= \hat i(4 + 4) - \hat j(12 - 4) + \hat k(-6 - 2)$$= 8\hat i - 8\hat j - 8\hat k$Now,the magnitude is given by:$|\overrightarrow A 	imes \overrightarrow B | = \sqrt{(8)^2 + (-8)^2 + (-8)^2}$$= \sqrt{64 + 64 + 64}$$= \sqrt{3 	imes 64}$$= 8\sqrt 3 $

If $\overrightarrow A = 3\hat i + \hat j + 2\hat k$ and $\overrightarrow B = 2\hat i - 2\hat j + 4\hat k$,then the value of $|\overrightarrow A \times \overrightarrow B |$ will be:

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