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  4. The equation of a plane passing through the line of intersection of the planes x+y+z=5,2 x-y+3 z=1 and parallel to the line y=z=0 is.

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Q. The equation of a plane passing through the line of intersection of the planes $x+y+z=5,2 x-y+3 z=1$ and parallel to the line $y=z=0$ is.

Three Dimensional Geometry

Solution:

The line $y=z=0$ is $x$-axis which has D.R.'s $<1,0,0>$
Let the required plane which is parallel to $x=$ axis be
$P ;(\lambda+2) x +(\lambda-1) y +(\lambda+3) z -(5 \lambda+1)=0$
So the product of D.R. 's will be zero
i.e., $\lambda+2=0$ and the plane $P$ will be
$P:-3 y+z+9=0$ or $3 y-z=9$