# [SOLVED] How to find vector of right triangle w/ 3 pts

• March 6th 2010, 04:23 AM
thekrown
[SOLVED] How to find vector of right triangle w/ 3 pts
A (3,0,2)
B (4,3,0)
C (8,1,-1)

How do i check to see if these are part of a right triangle and which vertex is the right triangle?

I can find cross products and dot products and distances between points and point and a line, but I do not understand the wording of this problem. What must I do?
• March 6th 2010, 04:25 AM
Prove It
Quote:

Originally Posted by thekrown
A (3,0,2)
B (4,3,0)
C (8,1,-1)

How do i check to see if these are part of a right triangle and which vertex is the right triangle?

I can find cross products and dot products and distances between points and point and a line, but I do not understand the wording of this problem. What must I do?

Find vectors $AB, BC, AC$ and take all three dot products.

If any of them is 0, then you have a right angle.
• March 6th 2010, 04:41 AM
thekrown
Alright so I found them:

vectors:
AB (1,3,-2)
BC (4,-2,-1)
AC (5,1,-3)

dot products:
AB.BC = 4-6+2 = 0 <---
BC.AC = 20 -2 +3 = 21
AB.AC = 5 + 3 + 6 = 14

So to answer this question correctly, the vertex at which the right triangle is the dot product AB.BC?

How do I formulate this in words... do I say "the vertex at which the right triangle is the dot product AB.BC"?
• March 6th 2010, 04:50 AM
HallsofIvy
Vector AB is from A to B. Vector BC is from B to C. What point of the triangle do those have in common?
• March 6th 2010, 04:54 AM
thekrown
Ah I see it, so the point B, common to both, is the point where the angle is a right angle. Point B is the "corner" where the angle is 90 degrees.