Question

Vector problem: I’m trying to determine if the mentioned vertices are right triangle.

Answer 1

A(4,5-3)
B(3,2,-1)
C(7,0,-2)

AB=(3-4)i+(2-5)j+(-1+3)k
=-i-3j+2k=<-1,-3,2>

BC=(7-3)i+(0-2)j+(-2+1)k
=4i-2j-k=<4,-2,-1>

AC=(7-4)i+(0-5)j+(-2+3)k
=3i-5j+k=<3,-5,1>

AB*BC=-1*4+-3*-2+2*-1=1
AB*AC=-1*3+-3*-5+2*1=14
BC*AC=4*3+-2*-5+-1*1=21

(pardon my missing vector arrows, and hats on i,j,k)

Answer 2

Somehow, by using the dot product, i couldn't get zero in either AB*BC, AB*AC, and BC*A

Answer 3

There's an error with my arithmetic i suppose.

Answer 4

have u learnt how to take the dot product

Answer 5

you did make an error when you did the dot product

Answer 6

either that or see the length are in the form a^2+b^2=c^2

Answer 7

Oh okay. Thanks! This semester is like my first time learning the doc product, can't remember it from precal. I'll go over what i did. Thanks again @dan815 and @jim_thompson5910 .

Answer 8

you have the right steps, just a silly arithmetic mistake

Answer 9

Lol Alright, i feel good now. I was afraid that i didn't know what i'm trying to solve for.

Answer 10

the dot product and the cow law are very closely related

Answer 11

AC*BC=-1*4+-3*-2+2*-1=0

Answer 12

I think you mean AB*BC=-1*4+-3*-2+2*-1=0 right?

Answer 13

Yes that AB and BC

Answer 14

Sorry xD

Answer 15

that's ok. I'm getting the same result. So AB is orthogonal (ie perpendicular) to BC