Question

Find the Cartesian equation of the following equation of the plane:

[x, y, z] = [3, 1, 5] + s[−2, 3, −1] + t[2, 1, −2]

Answer 1

My answer came out to be 5x+6y+8z-61=0. Is that correct?

Answer 2

(-2,3,1) x (2,1-2)
= (-5,-6,-8)

n = (5,6,8)
5(x-3) + 6(y-1) + 8(z-5)
5x + 6y + 8z - 61

Answer 3

Does that make sense?

Answer 4

How would you suggest I go about this? I was kinda winging it xD

Answer 5

My logic was s and t are vectors. I crossed them to get the normal and then just plugged in the point. Which gave me the resultant that I got.

Answer 6

Now that I think about it, doesn't it make sense?