is the plane perpendicular?

[hayood]

Determine whether the planes are perpendicular.
b) (3,0,-2) dot product (x+4,y-7,z+1)=0; (1,1,1) dot product (x,y,z)=0

i dont know should i only take (3,0,-2) dot product (1,1,1) ?

 

[JeffWest]

In the problem statement that you gave you said

Determine whether the planes are perpendicular.
b) (3,0,-2) dot product (x+4,y-7,z+1)=0; (1,1,1) dot product (x,y,z)=0

Yes that is true.

The way I understand that is that they didn't give you the complete plane equations but gave you the normal vectors separate.
\(\displaystyle n_1=<3,0,2>\)
\(\displaystyle n_2=<1,1,1>\)
the dot product of two vectors says that they are perpendicular.

If the normal vectors are perpendicular then the planes are perpendicular. Does that make sence? Normal vectors are perpendicular to their planes by nature.
So if you take the dot product of the normal vectors and it equals zero then the planes are perpendicular.
The following shows what I mean