how do you calculate the intersection of a line and cylinder?

Question

where does the line

x=1+t, y=3-t, z=2t

intersect the cylinder x^2+y^2=16 ?

how do you solve this problem?

Answer 1

Substitute:
(1+t)²+(3-t)²=16
1+2t+t²+9-6t+t²=16
2t²-4t+10=16
t²-2t+5=8
t²-2t+1=4
(t-1)²=4
t-1=±2
t= 3 or -1

Substituting this back into your parametric equations yields intercepts at (4, 0, 6) and (0, 4, -2).