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A plane P passes through the line of intersection of the planes $2 x-y+3 z=2, x+y-z=1$ and the point $(1,0,1)$. What is the equation of the plane P? $\quad$
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Verified Answer
The correct answer is:
$5 x+2 y-5=0$
Eq. of plane through two given planes is:
$(2 x-y+3 z-2)+\lambda(x+y-z-1)=0$
It passes through $(1,0,1)$ $\therefore 3-\lambda=0 \Rightarrow \lambda=3$
Eq. of plane is:
$5 x+2 y-5=0$
$(2 x-y+3 z-2)+\lambda(x+y-z-1)=0$
It passes through $(1,0,1)$ $\therefore 3-\lambda=0 \Rightarrow \lambda=3$
Eq. of plane is:
$5 x+2 y-5=0$
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