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lat A be avector parallel to line of intersection of two planes P1 and P2 through origin. P1 is parallel to the vectors 2i+3k and 4j-3k and P2 is parallel to j-k and 3i+3j, then the angle between vector A and 2i+j-2k. ANS; 45 and 135 degree
P1 is parallel to vector 2i+3j & 4j-3k normal of P1 = (2i+3j)*(4j-3k) =-9i+6j+8k (let it be B) normal of plane P2 = (j-k)*(3i+3j) =-3i+3j+3k (let it be C) line of intersection of planes will be B*C A = B*C =(-9i+6j+8k)*(-3i+3j+3k) = -6i-3j-9k angle bw A & 2i+j-2k is cos@ = 1/(126)1/2 or @ = cos-1 (1/3sqrt14)
P1 is parallel to vector 2i+3j & 4j-3k
normal of P1 = (2i+3j)*(4j-3k)
=-9i+6j+8k (let it be B)
normal of plane P2 = (j-k)*(3i+3j)
=-3i+3j+3k (let it be C)
line of intersection of planes will be B*C
A = B*C
=(-9i+6j+8k)*(-3i+3j+3k)
= -6i-3j-9k
angle bw A & 2i+j-2k is
cos@ = 1/(126)1/2 or
@ = cos-1 (1/3sqrt14)
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