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Q.

Let A be vector parallel to line of intersection of planes P1 and P2. Plane P1 is parallel to the vectors 2j^+3k^ and 4j^3k^ and that P2 is parallel to j^k^ and 3i^+3j^ , then the angle between vector A and a given vector 2i^+j^2k^ is

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a

3π4

b

π2

c

π6

d

π4

answer is B, D.

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Detailed Solution

Normal to plane P1 is
n1=(2j^+3k^)×(4j^3k^)=18i^
Normal to plane P2 is
n2=(j^k^)×(3i^+3j^)=3i^3j^3k^
A is parallel to ±n1×n2=±(54j^+54k^)
 Angle between A and 2i^+j^2k^ is 
cosθ=±(54j^+54k^)(2i^+j^2k^)5423=±12θ=π4 (or) 3π4

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