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Assertion :A component of vector b=4ˆi+2ˆj+3ˆk in the direction perpendicular to the direction of vector a=ˆi+ˆj+ˆk is ˆiˆj. Reason: A component of vector in the direction of ^a=ˆi+ˆk is 2ˆi+2ˆj+2ˆk.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is C Assertion is correct but Reason is incorrect
Component of b in direction of a is |b|cosθ^a where θ is the angle between a and b.
cosθ=4+2+372
Thus, component along a=(29)987^i+^j+^k3=3(^i+^j+^k)
So, component in perpendicular direction of ^a is ^b3(^i+^j+^k)=^i^j.

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