The equation of the plane which is equally inclined to the lines x-12=y-2=z+2-1 and x+38=y-41=z-4 and passing through the origin is/are
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a
14x - 5y - 7z = 0
b
2x + 7y -z = 0
c
3x - 4y - z = 0
d
x + 2y - 5z = 0
answer is A.
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Detailed Solution
The plane is equally inclined to the lines. Hence, it is perpendicular to the angle bisector of the vectors2i^-2j^-k^ and 8i^+j^-4k^Vector along the angle bisectors of the vectors are2i^-2j^-k^3±8i^+j^-4k^9or 14i^-5j^-7k^9and-2i^-7j^+k^9Hence, the equations of the planes arel4x - 5y - 7z = 0 or 2x + 7y - z = 0