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Question

If ˆi,ˆj and ˆk are unit vectors along x, y and z – axes respectively, the angle θ between the vector ˆi+ˆj+ˆk and vector ˆi is given by

A

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B

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C

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D

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Solution

The correct option is A

cosθ=(ˆi+ˆj+ˆk).ˆi(ˆi2+ˆj2+ˆk2)1/2׈i=ˆi.ˆi+ˆj.ˆi+ˆk.ˆi(1+1+1)1/2×1=1+0+03=13
(ˆj.ˆi+ˆk.ˆi=0 and ˆi.ˆi=1)
Hence the correct choice is (a).

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