a) Find parametric equations for the line through (4, 1, 4) that is perpendicular to the plane x − y + 2z = 7. (Use the parameter t.)

Question

b) In what points does this line intersect the coordinate planes?
xy-plane?
yz-plane?
xz-plane?

Answer 1

the normal to the plane has direction cosines proportional to <1,-1,2>, so
x = 4+t
y = 1-t
z = 4+2t

xy-intercept:
z=0, so t = -2
(2,3,0)
and so on