prove a triangle with sides given by vectors to be a right angled triangle

[M-D]

here is the question:
Consider a triangle with corners A(2,1,4), B(6,-1,-4) and C(3,4,2).

a) use vectors to show that the triangle is right angled

b) At which corner is the right angle?

i do not know how to go about this question. your help will be greatly appreciated. thanks

[b^3]

Hint: If the dot product of two vectors is zero, then they are perpendicular, that is the angle between them is .

[M-D]

thanks b^3.
here are the results of the dot products:

A dot B=-5
A dot C=18
B dot C= 6

none of them are zero. is there any other way of solving this?

[b^3]

Remember those are the corners of the triangle, not the vectors that make it up. So you'd need to find the three vectors that have those start and endpoints. e.g. . Then take the dot product of those three vectors you find.
 
 
 

[lzxnl]

Alternatively you could work out the lengths of the three vectors formed by the three position vectors and show that these satisfy Pythagoras's relation.

[FlorianK]

here is the question:
Consider a triangle with corners A(2,1,4), B(6,-1,-4) and C(3,4,2).

a) use vectors to show that the triangle is right angled

b) At which corner is the right angle?

i do not know how to go about this question. your help will be greatly appreciated. thanks

First of all the triangle is not given by vectors. The triangle is given by the co-ordinates of the vertices A, B and C.

You need to find the vectors of the sides

So:




Now you just need to calculate the dot product of each of them so:
= ?₁
= ?₂
= ?₃

If a questionmark equals zero it has to be a  a right angled triangle