Question

Find an equation for the plane K that is parallel to N which is defined by the equation 4x-3y-6z=12 and passes through the point (2, 3, -1)

Answer 1

pull off the normal and plug in the point

Answer 2

parallel lanes have the same normal vectors

Answer 3

So, I would plug (2, 3, -1) into 4x-3y-6z and find what that equals then the equation for plane k is the 4x-3y-6z=the answer I just found?

Answer 4

first, write up the standard equation of a plane.

a(x-Px)+b(y-Py)+c(z-Pz)

the abc parts are the same as the coeefs in the other eq;

4, -3, -6

next, plug in the point they give you (Px,Py,Pz)