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Question

Let A be vector parallel to line of intersection of planes P1 and P2 through origin. P1 is parallel to the vectors 2^j+3^k and 4^j3^k and P2 is parallel to ^j^k and 3i+3^j, then the angle between vectors ¯¯¯¯A and 2^i+^j2^k is

A
π2
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B
π4
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C
π6
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D
3π4
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Solution

The correct options are
C 3π4
D π4
Vector AB is parallel to [(2^j+3^k)×(4^j3^k]×[(^j^k)×(3^i+3^j)]=54(^j^k)
Let θ is the angle between the vector, then cosθ=±(54+1083.542)=±12
Hence θ=π4, 3π4 .

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