Answer
(a) $(x,y,z) = (7, -3, 8)$
(b) $(x,y,z) = (-12,16, -11)$
Work Step by Step
(a) We can use the line of intersection to find the value of $n$:
$(x,y,z) = (-1,5,0) + n(1,-1,1)$
Since $x = 7$, the $x$ coordinate in the line of intersection must be $7$:
$-1+n(1) = 7$
$n = 8$
We can use the line of intersection to find the point in both planes:
$(x,y,z) = (-1,5,0) + n(1,-1,1)$
$(x,y,z) = (-1,5,0) + (8)(1,-1,1)$
$(x,y,z) = (-1+8,5+(-8),0+8)$
$(x,y,z) = (7, -3, 8)$
(b) We can use the line of intersection to find the value of $n$:
$(x,y,z) = (-1,5,0) + n(1,-1,1)$
Since $y = 16$, the $y$ coordinate in the line of intersection must be $16$:
$5+n(-1) = 16$
$n = -11$
We can use the line of intersection to find the point in both planes:
$(x,y,z) = (-1,5,0) + n(1,-1,1)$
$(x,y,z) = (-1,5,0) + (-11)(1,-1,1)$
$(x,y,z) = (-1-11,5+11,0-11)$
$(x,y,z) = (-12,16, -11)$
