Cartesian Equation and Parametric Equation Help

Question

I just need some help with a maths question that I am trying to get done for a maths tutorial homework sheet.

The question is... Let L be the line through D = (6,5,4) and E = (1,0,6), and let P be the plane with the cartesian equation:
x-3y+4z = 16

i) - find an equation for l in vector paremetric form ii) find the point of intersection of L and P

please help!

I don't even know where to begin.

Can you also please explain it in steps so that I can follow the logic.

Thanks in advance

Answer 1

If you have two points, $P$ and $Q$, the line through them is parameterized by $$ (1-t)P+tQ. $$ This will give you three coordinate functions $x(t)$, $y(t)$, $z(t)$. Substitute those into the equation for the plane.