Question 941323: Show that vector n [2, 4, 6] is perpendicular to every vector on the plane:
2x + 4y + 6z = 12
I'd offer what I've tried, but honestly, I have no clue. My textbook doesn't seem to illustrate a similar problem, and I cannot find a similar solution in my notes.
Please assist! It's greatly appreciated!
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Let  and  be two vectors in the plane.
=( , , )
=( , , )
Since they're in the plane,
1.
2.
If you subtract eq. 1 from eq. 2,
3.
.
.
.
If they are perpendicular to the normal vector, then the dot product of each vector with the normal will be zero.
(,,)*( , , )=
4.
.
.
(,,)*(,,)=
5.
So then if I subtract the two dot products,
6.
Comparing eq. 6 to eq. 3, you recognize they are identical.
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