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August 24, 2016
Posted by **Lulu** on Monday, July 7, 2008 at 12:39pm.

- Calculus -
**Reiny**, Monday, July 7, 2008 at 5:23pmYou are on the right track, so (3,2,6) must be a direction vector on your new plane.

you also have two points M(1,2,3) and N(3,2,-1), so the vector MN or (2,0,-1) is another direction vector.

So by taking the cross-product of vectors (3,2,6) and (2,0,-1) I got (2,-6,1)

which must be the normal to the new plane.

So the new plane has equation

2x - 6y + z = k

but M(1,2,3) lies on it, so 2 - 12 - 1 = k

k = -7

The new plane has equation 2x - 6y + x = -7

Check:

1. Both M and N satisfy the new equation

2. Is the dot-product of their normals zero? (3,2,6)∙(2,-6,1) = 6-12+6 = 0

There you go!- typo correction -
**Reiny**, Monday, July 7, 2008 at 5:28pmmy line

<but M(1,2,3) lies on it, so 2 - 12 - 1 = k >

should say :

but M(1,2,3) lies on it, so 2 - 12**+ 3**= k

- typo correction -
- Calculus -
**Lulu**, Monday, July 7, 2008 at 9:16pmI appreciate the help, but you made another mistake. You got a wrong answer, it should be (2,0,-4) not (2,0,-1) so thus, you used the wrong information. But thanks, I know what to do now :)