Hi i've been trying to solve this question for a couple of days but I just
cant seem to be able to figure it out. The vertices of a triangle are 
A(-3,1,2), B(1,-3,-1), and C(3,-1,-1)verify that the triangle is a right
-angled triangle.

You need to show that the dot product of two of these three vectors

1. The vector from A to B
2. The vector from A to C
3. The vector from B to C
 
is zero.

1. The vector from A to B is < 1-(-3), -3-1, -1-2 > OR < 4, -4, -3 >
2. The vector from A to C is < 3-(-3), -1-1, -1-2 > OR < 6, -2, -3 >
3. The vector from B to C is < 3-1, -1-(-3), -1-(-1) > OR < 2, 2, 0 >

The dot product of the 1st and 2nd vectore is 4(6)+(-4)(-2)+(-3)(-3) =
24 + 8 + 9 =  41, WHICH IS NOT ZERO

The dot product of the 1st and 3rd vectore is 4(2)+(-4)(2)+(-3)(0) =
8 - 8 + 0 =  0.  That's all we need!  We don't need to find the dot 
product of the 2nd and 3rd (which will not be 0.  The 1st and 3rd 
vectors are perpendicular so two of the sides of triangle ABC are
perpendicular.    

Edwin