Question

Find the normal form of the equation of the plane that passes through P = (0,-2,5) and is parallel to the plane with general equation 6x-y+2z = 3

Answer 1

if two planes are parallel they have the same normal vectors
agree?

Answer 2

Yes.

Answer 3

and what is that vector?

Answer 4

The normal vector would be perpendicular to the line in the question.

Answer 5

what line in the question?
there are only two planes...

Answer 6

The normal vector is perpendicular to the planes.

Answer 7

right, and what is it?

Answer 8

n (dot) x = n (dot) p

Answer 9

I mean you need to be able to explicitly tell me what n is or you cannot proceed

Answer 10

for an equation of the form\[ax+by+cz=d\]the normal vector is\[\vec n=\langle a,b,c\rangle\]

Answer 11

6x - y +2z = 12

Answer 12

Is that right?

Answer 13

the normal vector should just be the coefficients of the variables, so no

Answer 14

The normal vector would just be 6 - 1 + 2.

Answer 15

n=(6,-1,2) yes

Answer 16

now you can use your formula
n (dot) x = n (dot) p

Answer 17

I think you have the same lame teacher as someone else I just helped with a similar problem who was using similar notation :P

Answer 18

Well that helps.

Answer 19

do you know how to use that formula?

Answer 20

6 x 6 0
-1(dot) y = -1 (dot) -2
2 z 2 5

Answer 21

good, which is what?

Answer 22

<6x, -y, 2z> = 12

Answer 23

that should not be a vector after taking the dot product; the dot product produces scalars only

Answer 24

the components need to be added together

Answer 25

...talking about the left side...

Answer 26

6x-1y+2z=12

Answer 27

very good, and you're done!

Answer 28

Thank you!

Answer 29

welcome!