how do u write the parametric equation of the planes through these pts: (0,0,0), (0,2,0) & (1,0,2)?

Answer 1

First let's find two vectors that lie in the plane.

u = <0,2,0> - <0,0,0> = <0,2,0>
v = <1,0,2> - <0,0,0> = <1,0,2>

One of the points in the plane is (0,0,0).

The equation of the plane is:

r = (0,0,0) + su + tv
where s and t are scalars that range over the real numbers.

The parametric equations of the plane are:

x = 0 + 0s + 1t
y = 0 + 2s + 0t
z = 0 + 0s + 2t

Simplify.

x = t
y = 2s
z = 2t