Question

Prove that the vectors u = 3i + j - 2k , v = -i + 3j+ 4k and w = 4i - 2j - 6k can form the sides of a triangle

Answer 1

You learn linear algebra?

Answer 2

Prove:
1) Try w+v, its equal u. Isn't that suspicious? This proves that these three vectors are side of a triangle. But wait! we don't know if they are in the same plane yet :)
2) To prove all of them are in the same plane, find determinant of the 3x3 matrix. If it is zero, then you got your answer.

Answer 3

@imron07 the determinant of the 3 by 3 matrix is also zero...how does that make them to be in the same plane?

Answer 4

This means one of the the three vectors aren't independent (or span new dimension) from the other two. In other word, you can make one of them by combyning the other two.
Say:
a*v+b*w=u
You can find that a=b=1.
Well, the second step isn't really neccesary actually (because by guessing, you already know that v+w=u).