Answer
(a) $(x,y,z) = (2+n, -3+2n, 5+4n)$
(b) $(x,y,z) = (0, -7, -3)$
Work Step by Step
(a) We can write an equation for this line:
$(x,y,z) = (2,-3,5)+n(1,2,4) = (2+n, -3+2n, 5+4n)$
(b) We can find the required value of $n$:
$2x-y+5z=-8$
$2(2+n)-(-3+2n)+5(5+4n)=-8$
$4+2n+3-2n+25+20n=-8$
$32+20n=-8$
$20n=-8-32$
$20n=-40$
$n=-2$
We can find the point of intersection:
$(x,y,z) = (2+n, -3+2n, 5+4n)$
$(x,y,z) = (2+(-2), -3+2(-2), 5+4(-2))$
$(x,y,z) = (0, -7, -3)$
