Let L be the line passing through the point P1,2,0 and perpendicular to the plane r¯⋅3i¯+4k¯=0 if line intersects the plane r¯⋅i¯−j¯+k¯=13 at point Q, then Q is
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a
3,−6,4
b
−2,−4,1
c
7,2,8
d
4,0,9
answer is C.
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Detailed Solution
The equation of the line passing through the point P1,2,0and perpendicular to the plane r¯⋅3i¯+4k¯=0 is x−13=y−20=z−04=kThe general point on the above line is3k+1,2,4kThis point lies on the planex−y+z=13It implies that 3k+1−2+4k=137k=14k=2 Therefore, the pointQ7,2,8