Let a→$$=2i^-j^+k^$$, b→$$=i^+2j^-k^$$ and c→$$=i^+j^-2k^$$ . A vector in the plane of b→ and c→ , whose projection on a→ is of magnitude $$2/3$$ is

Correct option is 12i^+3j^−3k^

Questions

$Let \vec{a} = 2 \hat{i} - \hat{j} + \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - \hat{k} and \vec{c} = \hat{i} + \hat{j} - 2 \hat{k} . A vector in the plane of \vec{b} and \vec{c},$ $whose projection on \vec{a} is of magnitude \sqrt{2 / 3} is$

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detailed solution

Correct option is A

Let d→=b→+λc→Then length of the projection of d¯ on a¯ is a¯·d¯a⇒a→·d→|a→|=±23⇒λ=1⇒d→=2i^+3j^−3k^

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Let a→=2i^-j^+k^, b→=i^+2j^-k^ and c→=i^+j^-2k^ . A vector in the plane of b→ and c→ , whose projection on a→ is of magnitude 2/3 is

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$Let \vec{a} = 2 \hat{i} - \hat{j} + \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - \hat{k} and \vec{c} = \hat{i} + \hat{j} - 2 \hat{k} . A vector in the plane of \vec{b} and \vec{c},$ $whose projection on \vec{a} is of magnitude \sqrt{2 / 3} is$