Elementary Geometry for College Students (6th Edition)

(a) $(x,y,z) = (2+n, -3+2n, 5+4n)$ (b) $(x,y,z) = (0, -7, -3)$
(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: $(x,y,z) = (2+n, -3+2n, 5+4n)$ $(x,y,z) = (2+(-2), -3+2(-2), 5+4(-2))$ $(x,y,z) = (0, -7, -3)$