(a)Is triangle ABC a right-angled triangle? Justify your answer.
[Note: A right-angled triangle is a triangle with one 90o internal angle.]
Vector AB is ( 3, 6 , 1)
Vector BC is ( 0 , -7 , -4)
Vector CA is ( -3 , 1 , 3)
No.
Do what I said.
Find $\displaystyle A\cdot B$, $\displaystyle A\cdot C$ and $\displaystyle B\cdot C$, and see if any of these dot products are 0. If so, you have a right angle.
If you do not know anything about dot products (also known as scalar products) I suggest you do a Google search.