JEE Main2012MathematicsThree Dimensional GeometryActual

The equation of a plane containing the line x+1 -3 = y-3 2 = z+2 1 and the point (0,7,-7) is

Options

Ax+y+z=0
Bx+2 y+z=21
C3 x-2 y+5 z+35=0
D3 x+2 y+5 z+21=0

Correct answer

A. x+y+z=0

Step-by-step solution

The equation of the plane containing the line x+1 -3 = y-3 2 = z+2 1 is a (x+1)+b(y-3)+c(z+2)=0 where -3 a+2 b+c=0 This passes through (0,7,-7) aligned & a(0+1)+b(7-3)+c(-7+2)=0 & a+4 b-5 c=0 ...(B) aligned On solving equation (A) and (B) we get a=1, b=1, c=1 Required plane is aligned & x+1+y-3+z+2=0 & x+y+z=0 aligned

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