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Question

Let a=^i+^j+^k, b=^i^j+^k and c=^i^j^k be three vectors. A vector v in the plane of a and b, whose projection on c is 13, is given by

A
^i3^j+3^k
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B
3^i3^j^k
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C
3^i^j+3^k
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D
^i+3^j3^k
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Solution

The correct option is C 3^i^j+3^k
A vector v in the plane of a and b is v=a+λb
v=(^i+^j+^k)+λ(^i^j+^k)
Projection of v on c =13
v.cc=13
(1+λ)(1λ)(1+λ)3=13
(1+λ)(1λ)(1+λ)=1
λ=2
So, v=3^i^j+3^k

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