Let \( a = i + j + k,\; b = i - j + k\) and c = î - ĵ - k̂ be three vectors. A vector \( v\) in the plane of \( a\) and \( b\) whose projection on \( c | c| \) is \( 1 3...

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Question 20

Mathematics Scalar and Vector Products Hard

Let \(\rm \vec a =\hat i +\hat j +\hat k,\; \vec b =\hat i -\hat j + \hat k\) and c = î - ĵ - k̂ be three vectors. A vector \(\rm \vec v\) in the plane of \(\rm \vec a\) and \(\rm \vec b\) whose projection on \(\rm \frac {\vec c} {|\vec c|}\) is \(\frac 1 {\sqrt 3},\) is

(A) 3î - ĵ + 3k̂

(B) î - 3ĵ + 3k̂

(C) 5î - 2ĵ + 5k̂

(D) 2î - ĵ + 3k̂

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Correct Solution: Option A

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