Question

use vectors to decide whether the triangle with vertices p(1,-3,-2), Q(2,0,4), R(6,-2,-5) is right-angled.

Answer 1

Well, I'm pretty sure you can at the very least use the pythagorean theorem for 3D triangles to figure out if it is true. From there, you can just graph in 3D and show it that way. What's the difficulty with doing that?

Answer 2

im guessing using dot product, but i got confused when they give points.

Answer 3

if i dot P and Q, it gives me whether they are parallel, or perpendicular at the origin. which does not work.

Answer 4

is Pythagorean for 3d same as for 2d? a^2+b^2=c^2 ?

Answer 5

It's

\(d^2 = x^2 + y^2 + z^2\)

Answer 6

ye got that. can you show me how to do it though-

Answer 7

I think i did it : very unclear but i got the right answer.

Answer 8

When you have two points of the form (x, y, z) and (x', y',z') the vector connecting them is given by R = (x'-x) i +(y'-y) j + (z'-z) k
Use this relation to find the vectors for each side then you can check with the Dot product of all possible pairs if you get a zero; that would tell you that those two sides are perpendicular to each other.

Answer 9

However, when you take dot product of all the 3 sides, none give you 0.. But i toke those 3 sides and picked 2 sides for the leg, and used Pythagorean to find the third side. if the third side is equal to the magnitude of the third side. Than it means the Pythagorean worked. so it must be a right triangle. This is a bad way to do it. but that's all i know right now- kinda lost.

Answer 10

It's not a right triangle

Answer 11

Similarly find the other two sides, PR and QR, then find PQ.QR; PQ.PR; and QR.PR; if any of these is zero it tells you that the two sides are perpendicular to each other. (PQ.QR = dot product of vectors PQ and QR)