# Use vectors to determine if points are @ right angle

• Apr 15th 2008, 09:15 PM
angel.white
Use vectors to determine if points are @ right angle
Use vectors to decide whether the triangle with vertices P(1,-3,2), Q(2,0,-4) and R(6,-2,-5) is right angled.

I have a theorem in my book that says two vectors are orthogonal (perpendicular) if and only if their dot product is equal to zero. But I seem to be having difficulty turning them into vectors. Also, it seems that there should be 3 different sets of vectors that I could choose, how do I determine which are the best choice without graphing it out? ...and is there a method where that doesn't matter?
• Apr 15th 2008, 09:46 PM
Kalter Tod
Quote:

Originally Posted by angel.white
Use vectors to decide whether the triangle with vertices P(1,-3,2), Q(2,0,-4) and R(6,-2,-5) is right angled.

I have a theorem in my book that says two vectors are orthogonal (perpendicular) if and only if their dot product is equal to zero. But I seem to be having difficulty turning them into vectors. Also, it seems that there should be 3 different sets of vectors that I could choose, how do I determine which are the best choice without graphing it out? ...and is there a method where that doesn't matter?

You just need to form 3 separate vectors $\displaystyle \vec{PQ}$, $\displaystyle \vec{QR}$, and $\displaystyle \vec{QP}$ by finding the displacements between the involved vectors in all 3 dimensions for example $\displaystyle \vec{PQ}=(-1, 3, 6)$and then you can just use the formula for finding Cross Products