If a→ = 2i^+3j^−4k^, b→ = i^+j^+k^, c→ = 4i^+2j^+3k^ then a→×b→×c→= ________

a→×b→×c→=a→ . c→b→ − a→ . b→ c→= 5

If a→ = 2i^+3j^−4k^, b→ = i^+j^+k^, c→ = 4i^+2j^+3k^ then a→×b→×c→= ________

a→×b→×c→=a→ . c→b→ − a→ . b→ c→= 5

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If $\vec{a} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k},$ $\vec{b} = \hat{i} + \hat{j} + \hat{k},$ $\vec{c} = 4 \hat{i} + 2 \hat{j} + 3 \hat{k}$ then $|\vec{a} \times (\vec{b} \times \vec{c})| =$ ________

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$\sqrt{10}$

$\sqrt{5}$

answer is D.

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Detailed Solution

$|\vec{a} \times (\vec{b} \times \vec{c})| = |(\vec{a} . \vec{c}) \vec{b} - (\vec{a} . \vec{b}) \vec{c}|$
= $\sqrt{5}$

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If a→ = 2i^+3j^−4k^, b→ = i^+j^+k^, c→ = 4i^+2j^+3k^ then a→×b→×c→= ________

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If $\vec{a} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k},$ $\vec{b} = \hat{i} + \hat{j} + \hat{k},$ $\vec{c} = 4 \hat{i} + 2 \hat{j} + 3 \hat{k}$ then $|\vec{a} \times (\vec{b} \times \vec{c})| =$ ________