Find Vector Perpendicular to Plane

• MHB
• brinlin
In summary, a vector perpendicular to a plane is a vector that is at a 90 degree angle to the plane and does not lie on the plane itself. To find this vector, two non-parallel vectors on the plane can be used with the cross product. It is important to find a vector perpendicular to a plane for determining its orientation and direction. There can be infinitely many vectors perpendicular to a plane, and they are all parallel to the plane's normal vector.
brinlin
Find a vector that is perpendicular to the plane passing through the points P (1, 2, 3), Q (2, 3, 1), and R (3, 1, 2).

vector product yields a vector perpendicular to two vectors ...

$\vec{PQ} \times \vec{PR}$

I'm sorry I don't really understand.

brinlin said:
I'm sorry I don't really understand.

you don't understand, or you don't know what a vector product is and how to calculate it?

$\vec{PQ} = (1,1,-2)$
$\vec{PR} = (2,-1,-1)$

$\vec{PQ} \times \vec{PR} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1& 1 & -2 \\ 2 &-1 &-1 \\ \end{vmatrix}$

1. What is a vector perpendicular to a plane?

A vector perpendicular to a plane is a vector that is at a right angle to every vector in the plane. This means that the dot product of the perpendicular vector and any vector in the plane will be equal to zero.

2. How do you find a vector perpendicular to a plane?

To find a vector perpendicular to a plane, you can use the cross product of two vectors that lie in the plane. The resulting vector will be perpendicular to both of these vectors and therefore, perpendicular to the plane.

3. Can there be more than one vector perpendicular to a plane?

Yes, there can be an infinite number of vectors that are perpendicular to a plane. This is because any vector that is parallel to the plane can be used to find a perpendicular vector using the cross product.

4. How do you determine the direction of the perpendicular vector?

The direction of the perpendicular vector can be determined by using the right-hand rule. This rule states that if you curl the fingers of your right hand in the direction of the first vector and then curl them towards the second vector, your thumb will point in the direction of the resulting perpendicular vector.

5. Why is finding a vector perpendicular to a plane important?

Finding a vector perpendicular to a plane is important in many applications, such as computer graphics, physics, and engineering. It allows us to find the normal vector to a surface, which is useful in calculating angles, determining forces, and solving equations involving planes.

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