NDA2012MathematicsThree Dimensional GeometryActual

What is the equation to the plane through (1,2,3) parallel to 3 x+4 y-5 z=0 ?

Options

A3 x+4 y+5 z+4=0
B3 x+4 y-5 z+14=0
C3 x+4 y-5 z+4=0
D3 x+4 y-5 z-4=0

Correct answer

C. 3 x+4 y-5 z+4=0

Step-by-step solution

Let equation of plane parallel to 3 x+4 y-5 z=0 is 3 x+4 y-5 z+ =0 it passes through (1,2,3) 3(1)+4(2)-5(3)+ =0 aligned & & 3+8-15+ & =0 & & & =4 aligned equation of plane is 3 x+4 y-5 z+4=0 .

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