Thread: [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?

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 and take all three dot products.

If any of them is 0, then you have a right angle.

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"?

Vector AB is from A to B. Vector BC is from B to C. What point of the triangle do those have in common?

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.