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

how do you know in which directions the vectors are?

Answer 2

When vertices are given in this form it is assumed, that P(1,-3,-2) is really OP(1,-3,-2) meaning from the Origin to point P. Thus to find (example) vector PQ, u will need to take OQ-OP.

Answer 3

move it to the origin :)

P(1,-3,-2) Q(2,0,-4) R(6,-2,-5)
-1 3 2 -1 3 2 -1 3 2
-------------------------------
0,0,0 1,3,-2 5,1,-3

dot product the nonzero vectors to see if they get 0

Answer 4

do this for each vertex or unti you find a set that is 0ed

Answer 5

but why do we choose P - Q instead of Q - P ? for the vector

Answer 6

your just moving this thing; you need to do it for all 3 points

Answer 7

etc

Answer 8

ideally if this thing had points at the origin youd be able to read the other 2 AS vectors