Question

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

• A. $3x-z=9$
• B. $3y-z=9$
• C. $x-3z=9$
• D. $y-3z=9$

Answer 1

Answer: (B)

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
$P:-3y+z+9=0$ or $3y-z=9$