Question

Find an equation of the plane.
The plane through the origin and the points (2,-4,6) and (5,1,3). does that mean i use the point (0,0,0) because i tried that and the dot product is perpendicular to everything at 0 i think

Answer 1

Yes you can use (0,0,0) as a point on the plane.
Here, you could also take the cross-product of the two vectors to get the normal vector.

Answer 2

Thats what i did so i used the point (0,0,0) and vector A(2,-4,6) an B(5,1,3) and did AxB to get the normal vector

Answer 3

equation of plane is:
\[ax +by+cz = d\]
plug in the 3 points to find the coefficients
since it goes through origin, this means that constant d = 0

Answer 4

What did you get for the cross product?

Answer 5

those are points...not vectors

Answer 6

-18i+24j-22k

Answer 7

yea but i used (0,0,0) as the origin so once you subtract the other two points they are the same, is that allowed

Answer 8

@dumbcow
OA=<2,-4,6>, OB=<5,1,3>
OAxOB gives you the normal to the plane.
I get <-18.,24.22>

Answer 9

You could also reduce it to
<-9,12,11>
and substitute in the plane equation with d=0 as @dumbcow mentioned.

Answer 10

ahh i see ...yes i get <-9,12,11> for a,b,c as well

Answer 11

@carr099 : everything's cool?

Answer 12

yea