Question

If the coordinates of the point where the line $x-2y+z-1=0=x+2y-2z-5$ intersects the plane $x+y-2z=7$ is $(\text{α},\text{β},\text{γ}),$ then find the value of $(|\text{α}|+|\text{β}|+|\text{γ}|)$

Answer 1

Answer: 7

The required point is the point of intersection of the three planes.
$x+y-2z=\mathrm{7.......}(1)$
$x-2y+z=\mathrm{1.......}(2)$
$x+2y-2z=\mathrm{5........}(3)$
$\therefore$ From $(3)-(1)\Rightarrow y=-2$
From $2\times (2)+(1)\Rightarrow 3x-3y=9\Rightarrow x=1$
So, from $(1),z=-4$ Hence the point is $(1,-2,-4)=(\text{α},\text{β},\text{γ})$ Hence $|\text{α}|+|\text{β}|+|\text{γ}|$
$=|1|+|-2|+|-4|=7$