# Cross Products

## Homework Statement

The whole problem is :
Find eqn of plane through (2, 0, 2) perpendicular to vectors <1, -1, 2> and <-1, 1, 0>

I am trying to figure out if I am making an error with cross products here...

Find the normal (perpendicular) vector of <1, -1, 2> and <-1, 1, 0>

## Homework Equations

Cross products equation... <1, -1, 2> X <-1, 1, 0>

## The Attempt at a Solution

Normal Vector: <-2, -3, 0>

So the plane equation would be
-2(x-2) -3(y-0)+0(z-2) =0
-2x-3y=4

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SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

The whole problem is :
Find eqn of plane through (2, 0, 2) perpendicular to vectors <1, -1, 2> and <-1, 1, 0>

I am trying to figure out if I am making an error with cross products here...

Find the normal (perpendicular) vector of <1, -1, 2> and <-1, 1, 0>

## Homework Equations

Cross products equation... <1, -1, 2> X <-1, 1, 0>

## The Attempt at a Solution

Normal Vector: <-2, -3, 0>

So the plane equation would be
-2(x-2) -3(y-0)+0(z-2) =0
-2x-3y=4
It's impossible for a plane to be perpendicular two two vectors which are not parallel to each other.

Do you mean that the normal to the plane is perpendicular to those two vectors?

I think I worded it incorrectly. Mostly I am interested in the cross products and if that particular cross product is correct. IE <1,-1,2> X <-1,1-0> = <-2, 3, 0>

ignore the rest of it...

Mark44
Mentor
I think I worded it incorrectly. Mostly I am interested in the cross products and if that particular cross product is correct. IE <1,-1,2> X <-1,1-0> = <-2, 3, 0>
ignore the rest of it...
No, it's not correct. You can check your work by dotting your result vector with each of the two vectors that make up the cross product. The result vector should be perpendicular to each of the other two, meaning that both dot products should be zero.

If you can't figure it out, show us your calculations.