Unit Vector Perpendicular to a Triangle?

[neotriz]

Homework Statement

Given: P=(1,-2,3), Q=(-4,2,5) and S=(2,1-4)

Find a unit vector that is perpendicular to triangle PQS

Homework Equations

Cross and Dot Product

The Attempt at a Solution

Correct me if I'm doing wrong. I have two solutions that I've thought:

1)What I would do is find the dot product of S and P and using that result, cross product with Q.

or

2)Find two dot products of two opposite triangle sidesand cross product on those.


Just want to make sure I am doing right

 

[Office_Shredder]

If you take a dot product, you're left with a scalar. The cross product requires vectors to be calculated.

You have the right idea of using the cross product though. One of the fundamental properties of the cross product is that $v_1 \times v_2$ is perpendicular to both v₁ and v₂. So you want to find two vectors from your triangle such that, if you get a vector perpendicular to both of them, you get a vector perpendicular to the triangle.

 

[neotriz]

I forgot that in dot product it gives you scalar result

How about this then:

I find P to S vector difference , which will result a vector of <-1, -3, -7> and using that vector, I cross product with Q

 

[Office_Shredder]

I forgot that in dot product it gives you scalar result

How about this then:

I find P to S vector difference , which will result a vector of <-1, -3, -7>

This is good. Taking the difference between S and P gives a vector that's pointing along one of the edges of the triangle, so is parallel to the triangle

and using that vector, I cross product with Q

On the other hand, is Q parallel to the triangle?