How these 3 vectors form a right triangle? $ A = 2\hat{i} -2\hat{j} + 3\hat{k}$
$ B = 2\hat{i} -\hat{j} + 3\hat{k}$
$ C = \hat{i} -\hat{j} - \hat{k}$
My textbook demands that these 3 vectors form right triangle. Firstly, I think these 3 vectors don't form a triangle. 
Actual Condition for triangle : $ A\pm{B}\pm{C} = 0$ and this is flase for these 3 vectors.
Am I wrong?

Here's what I'd do:


*

*Determine which two vectors are perpendicular. You can use the dot product to test this.

*Verify as you suggested in your question that the three vectors add to zero. You'll need to find the right signs on the vectors. (A triangle has three line segments, but you're given three vectors, each of which has a direction that individually doesn't matter. So take one of the vectors as-is, and try the four possibilities for the signs of the other two when you add them up. You should win on one of them.)

