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Q.

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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a

2i^+3j^−3k^

b

2i^+3j^+3k^

c

2i^+j^+5k^

d

5i−6j−7k

answer is A.

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Detailed Solution

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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