Question

Determine a vector equation for the plane with Cartesian equation 3x-2y+z-6=0 .

Answer 1

First, you need its normal vector.
Have you got it? ^_^

Answer 2

(3, -2, 1).. then?

Answer 3

That's right.
Enclose it in <> so that you know it's a vector (and not referring to a point)

And SPEAKING OF POINTS, you also need a point on the plane.
It can be anything, but I suggest, you let x and y equal zero, and work out z.

Answer 4

oh ok:)
x=y=0, the point is (0,0,6)

Answer 5

Good... Now, take a look at this 'plane' (pardon my poor drawing skills)
Are you LOOKING AT IT ?!

Answer 6

yes, it's good:)

Answer 7

Good.. now, say, this is your point (0,0,6)

Answer 8

And THIS... is your NORMAL vector, <3,-2,1>

Answer 9

Now, ANY point on the plane..., let's call it (x , y , z)...

Answer 10

The vector IT makes with your known point, (0,0,6)...
Which is... <x-0 , y-0 , z-6>
or...
<x , y , -6>

Answer 11

This will ALWAYS be perpendicular to your normal vector: