Find the equation of the plane passing through intersection of the plane 4x-y+z=10 and x+y-z=4 and parallel to the line with direction ratios proportional to (2,1,1). Find also perpendicular Distance of (1,1,1) From this plane.

equation of the plane passing through the intersection of the plane 4x-y+z=10 and the plane x+y-z=4 is given by:

since the plane (1) is parallel to the line with the direction ratios proportional to (2,1,1)

therefore

substituting the value of λ in (1)

-5y+5z+6=0 i.e. 5y-5z-6=0...(1a)

(ii) let perpendicular distance of (1,1,1) from plane 1(a) be l.

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