Find an equation of a plane containing the line r=⟨0,4,4⟩+t⟨−3,−2,1⟩ which is parallel to the plane 1x−1y+1z=−5 in which the coefficient of x is 1.

Question

Find an equation of a plane containing the line  which is parallel to the plane  in which the coefficient of x is 1.

Answer 1

Parallel line equation: x - y + z = d

Point (0,4,4) belong to this plane: 0 - 4 + 4 = d; d = 0

So, this plane equation x - y + z = 0.

Let check point when t = 1 we have point (- 3, 2, 5)

We check now if it belong to plane: - 3 - 2 + 5 = 0, 0 = 0.

So, equation of plane: x - y ++ z = 0.