Question

Find the vector and cartesian equations of the plane passing through the points A(1, -2, 3) and B(-1, 2, -1) and is parallel to the line (x - 2)/2 = (y + 1)/3 = (z - 1)/4 

Answer 1

The vector equation of the plane is

i.e, (x – 1)[16 + 12] – (y + 2)(-8 + 8) + (z – 3)(-6 – 8) = 0 

28(x – 1) – 14(z – 3) = 0 

28x – 28 – 14z + 42 = 0 

28x – 14z + 14 = 0 

(÷ by 14) ⇒ 2x – z + 1 = 0