p→=2i^−3j^+k^.q→=i^+j^−k^ . If the vectors a→ and b→ are the orthogonal projections of p→ on q→ and q→ on p→ respectively, then 2a→×b→a→.b→=

a→×b→a→.b→=p→×q→p→.q→=2i^+3j^+5k^2

p→=2i^−3j^+k^.q→=i^+j^−k^ . If the vectors a→ and b→ are the orthogonal projections of p→ on q→ and q→ on p→ respectively, then 2a→×b→a→.b→=

a→×b→a→.b→=p→×q→p→.q→=2i^+3j^+5k^2

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$\vec{p} = 2 \hat{i} - 3 \hat{j} + \hat{k} . \vec{q} = \hat{i} + \hat{j} - \hat{k}$ . If the vectors $\vec{a}$ and $\vec{b}$ are the orthogonal projections of $\vec{p}$ on $\vec{q}$ and $\vec{q}$ on $\vec{p}$ respectively, then $2 \frac{\vec{a} \times \vec{b}}{\vec{a} . \vec{b}} =$

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$2 \hat{i} + 3 \hat{j} - 5 \hat{k}$

$2 \hat{i} - 3 \hat{j} + 5 \hat{k}$

$2 \hat{i} + 3 \hat{j} + 5 \hat{k}$

$3 \hat{i} - 2 \hat{j}$

answer is C.

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$\frac{\vec{a} \times \vec{b}}{\vec{a} . \vec{b}} = \frac{\vec{p} \times \vec{q}}{\vec{p} . \vec{q}} = \frac{2 \hat{i} + 3 \hat{j} + 5 \hat{k}}{2}$

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p→=2i^−3j^+k^.q→=i^+j^−k^ . If the vectors a→ and b→ are the orthogonal projections of p→ on q→ and q→ on p→ respectively, then 2a→×b→a→.b→=

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$\vec{p} = 2 \hat{i} - 3 \hat{j} + \hat{k} . \vec{q} = \hat{i} + \hat{j} - \hat{k}$ . If the vectors $\vec{a}$ and $\vec{b}$ are the orthogonal projections of $\vec{p}$ on $\vec{q}$ and $\vec{q}$ on $\vec{p}$ respectively, then $2 \frac{\vec{a} \times \vec{b}}{\vec{a} . \vec{b}} =$