Discover the Properties of Triangle ABC: Vertices, Lengths, and Angles

[shiri]

A=(1,-1,-6), B=(4,4,2) and C=(-2,2,-4) are the vertices of a triangle.

a) ||AB||^2 + ||BC||^2 = ||AC||^2
b) ||AB||^2 + ||BC||^2 - ||CA||^2 = 152
c) ||AB||^2 + ||BC||^2 + ||CA||^2 = 196
d) The triangle has a right angle at A
e) The triangle is a right triangle


a) T
b) F, should be sqrt152
c) F, should be sqrt196
d) Not sure
e) Not sure

Can somebody help me out here, please? I'll be very appreciated

 

[Mark44]

For a, b, and c, all your answers are wrong. What are you getting for |AB|^2, |BC|^2, and |AC|^2?

For d, if you know the lengths of each side of a triangle, how can you tell if a particular angle is a right angle?
For e, if you know the lengths of each side of a triangle, how can you tell whether any angle is a right angle?