Find the linear equation of the plane through the point (2,10,6) ( 2 , 10 , 6 ) and parallel to the plane 𝑥+5𝑦+3𝑧+4=0.

Question

Find the linear equation of the plane through the point  and parallel to the plane 

Answer 1

Normal vector to given plane and unknown plane the same: [1, 5, 3]. So, equation ofplane what we looking for:

1(x - 2) + 5(y - 10) + 3(z - 6) = 0; x + 5y + 3z - 70 = 0