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Question: If \(\overset{\rightarrow}{A} = 3\widehat{i} + \widehat{j} + 2\widehat{k}\) and \(\overset{\rightarr...

If A→=3i^+j^+2k^\overset{\rightarrow}{A} = 3\widehat{i} + \widehat{j} + 2\widehat{k} and B→=2i^−2j^+4k^\overset{\rightarrow}{B} = 2\widehat{i} - 2\widehat{j} + 4\widehat{k} then value of ∣A→×B→∣|\overset{\rightarrow}{A} \times \overset{\rightarrow}{B}| will be-

A

828\sqrt{2}

B

838\sqrt{3}

C

858\sqrt{5}

D

585\sqrt{8}

Answer

838\sqrt{3}

Explanation

Solution

\widehat{i} & \widehat{j} & \widehat{k} \\ 3 & 1 & 2 \\ 2 & - 2 & 4 \end{matrix} \right|$$ $$= 8\widehat{i} - 8\widehat{j} - 8\widehat{k}$$ ∴Magnitude of $$\overset{\rightarrow}{A} \times \overset{\rightarrow}{B} = |\overset{\rightarrow}{A} \times \overset{\rightarrow}{B}| = \sqrt{(8)^{2} + ( - 8)^{2} + ( - 8)^{2}} = 8\sqrt{3}$$