Question

Where does the line through (1,0,1) and (3,−2,5)intersect the plane x+y+z=10?

(x, y, z) =________?

Answer 1

going from the first point to the second
dx = 3
dy = -2
dz = 4
so my line direction is 3 i -2 j + 4 k
and my line in parametric form is
(1,0,1) + (3, -2, 4) t

at intersection
x = 1+3t
y = -2 t
z = 1+4t
and we know x + y + z = 10
2 + 5 t = 10
t = 8/5
so
x = 1 + 24/5 = 29/5
y = -16/5 = -16/5
z = 1 + 32/5 = 37/5
Check my arithmetic !!