Kinematics Question 259
Question: If $ \overrightarrow{A}=3\hat{i}+\hat{j}+2\hat{k} $ and $ \overrightarrow{B}=2\hat{i}-2\hat{j}+4\hat{k} $ then value of $ |\overrightarrow{A}\times \overrightarrow{B}| $ will be
Options:
A) $ 8\sqrt{2} $
B) $ 8\sqrt{3} $
C) $ 8\sqrt{5} $
D) $ 5\sqrt{8} $
Correct Answer: B $ \overrightarrow{A}\times \overrightarrow{B}= \begin{vmatrix} \hat{i} & \hat{j} & {\hat{k}} \\ 3 & 1 & 2 \\ 2 & -2 & 4 \\ \end{vmatrix} $ $ =(1\times 4-2\times -2)\hat{i}+(2\times 2-4\times 3)\hat{j}+(3\times -2-1\times 2)\hat{k} $ $ =8\hat{i}-8\hat{j}-8\hat{k} $ Magnitude of $ \overrightarrow{A}\times \overrightarrow{B}=|\overrightarrow{A}\times \overrightarrow{B}|=\sqrt{{{(8)}^{2}}+{{(-8)}^{2}}+{{(-8)}^{2}}} $ $ =8\sqrt{3} $
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