Q.

The vector equation of the line passing through (1,2,3) and parallel to the planes r¯.(i¯−j¯+2k¯)=5 and r¯.(3i¯+j¯+k¯)=6 is

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a

r¯=i¯+2j¯+3k¯+λ(−3i¯+5j¯+4k¯)

b

r¯=i¯+2j¯+3k¯+λ(3i¯+5j¯+4k¯)

c

r¯=i¯+2j¯-3k¯+λ(-3i¯+5j¯+4k¯)

d

r¯=i¯+2j¯+3k¯+λ(3i¯-5j¯+4k¯)

answer is A.

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Detailed Solution

a¯=i¯−j¯+2k¯;b¯=3i¯+j¯+k¯a¯×b¯=−3i¯+5j¯+4k¯line parallel to a¯×b¯ and passing through (1,2,3)r¯=(i¯+2j¯+3k¯)+λ(−3i¯+5j¯+4k¯)x=y=z...........(1)x=y2=z3...........(2)
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The vector equation of the line passing through (1,2,3) and parallel to the planes r¯.(i¯−j¯+2k¯)=5 and r¯.(3i¯+j¯+k¯)=6 is