Wrtie a scalar equation given it's parametric equation.

Question

x = 3-2s+2t
y = 1+3s+t
z = 5-s-2t

Answer 1

Two direction vectors on the plane are (-2,3,-1) and (2,1,-2)
A normal to these is (5,6,8), their cross-product

so the plane has equation
5x + 6y + 8z = C
but (3,1,5) is a point on it, so
15 + 6 + 40 = C = 61

equation: 5x + 6y + 8z = 61