What is the Correct Cross Product for Finding a Normal Vector?

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In summary, it is impossible to find a plane that is perpendicular to two vectors that are not parallel to each other.
  • #1
char808
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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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  • #2
char808 said:

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?
 
  • #3
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...
 
  • #4
char808 said:
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.
 

1) What is the equation for a plane in standard form?

The equation for a plane in standard form is Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the x, y, and z variables, and D is a constant.

2) How do you solve a plane equation?

To solve a plane equation, you can use various methods such as substitution, elimination, or graphing. In this specific equation, you can rearrange the terms to solve for one variable, and then substitute that value into the other variable to find the solution.

3) What does the constant term represent in a plane equation?

The constant term in a plane equation represents the distance of the plane from the origin on the z-axis. In other words, the value of D determines how far the plane is from the origin in the z direction.

4) Can you graph a plane equation in two dimensions?

No, a plane equation cannot be graphed in two dimensions because it has three variables (x, y, and z) and requires a three-dimensional space to be accurately represented.

5) How can a plane equation be used in real-world applications?

Plane equations are used in various fields such as engineering, physics, and architecture to represent surfaces and geometric shapes in three-dimensional space. For example, they can be used to determine the slope of a roof or to calculate the trajectory of a projectile.

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