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Question

Given A=2^i+3^j and B=^i+^j. The component of vector A perpendicular to vector B and in the same plane as B is

A
12(^j^i)
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B
32(^j^i)
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C
52(^j^i)
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D
72(^j^i)
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Solution

The correct option is D 12(^j^i)
We know, (i+j)(ij)=0
Vector (ij) is perpendicular to B.
Let, (ij) = C
Now, (A.C)=(2i+3j)(ij)
The required component is:
(A.C)CC=2i+3j)(ij)(ij)ij
(A.C)CC=12(ij).......(since, C=(1+1)=2)
(A.C)CC=12(ji)

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