Find the Cartesian (scalar) equation for the plane whose vector equation is r=(1,3-4) + s(-2,8,5) + t(1,2,0)

Question

Please include steps and answer

Answer 1

We have parametric equation of plane: x = 1 - 2s + t, y = 3 + 8s + 2t, z = - 4 + 5s. Now we exlude parametr t

from 1st 2 equations: - 2x + y = 1 + 12s and from 3rd equation s = (z + 4)/5; so

-2x + y = 1 + 12(z + 4)/5, - 10x + 5y = 5 + 12z + 48, at last 10x - 5y + 12z + 53 = 0 is scalar equation of plane.