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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 vector 2^j+3^k and 4^j3^k and P2 is parallel to ^j^k and 3^i+3^j, then the angle between vector A and 2^i+^j2^k is

A
π2,3π4
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B
π4,π2
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C
π6,7π4
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D
π2,3π2
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Solution

The correct options are
A π2,3π4
C π4,π2
The normal vector of plane P1 is (2^j+3^k)×(4^j3^k), i.e. (6^i12^i).

Assuming that point (0,2,3) passes through the first plane we have the plane equation as 18x=0, i.e.x=0.

Similarly for P2, we have the normal vector as (^j^k)×(3^i+3^j)=(3^k3^j+3^i)

The equation of P2 thus becomes 3(x0)3(y1)3(z+1)=0, i.e.xyz=0

The line of intersection of two planes is passing through (0,0,0) and (0,1,1) , i.e. r=tytz.

So the point A can be (0,1,1) and so cosθ equals 332=12 implies θ=π4

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