Question

1) Parameterize the plane that contains the three points (2,3,−4), (2,−10,−4), and (40,5,5).
r⃗ (s,t)=

Answer 1

c^2=x^2+y^2+z^2

Answer 2

Let P=(2,3,−4), Q= (2,−10,−4), and R=(40,5,5)
compute the vectors
PQ=Q-P=(0,-13,0)
PR=R-P=(38,2,9)

Answer 3

One parameterization would be
r(s,t) =P + s PQ + t PR= (2 + 38 t, 3 - 13 s + 2 t, -4 + 9 t)

Answer 4

notice
that
r(0,0)=P
r(0,1)=R
r(1,0)= Q