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^j−3^k and P2 is parallel to ^j−^k and 3i+3^j, then the angle between vectors ¯¯¯¯A and 2^i+^j−2^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 C3π4 Dπ4 Vector AB is parallel to [(2^j+3^k)×(4^j−3^k]×[(^j−^k)×(3^i+3^j)]=54(^j−^k) Let θ is the angle between the vector, thencosθ=±(54+1083.54√2)=±1√2 Hence θ=π4,3π4 .