Proving that three particular vectors can form the sides of the line

Question

This question came up on a problem sheet I've been working on

Prove that the vectors $\mathbf{i} - \mathbf{k}$, $-\mathbf{i} + \mathbf{j} + 2\mathbf{k}$, $2\mathbf{i} - \mathbf{j} - 3\mathbf{k}$ can form the sides of the triangle.

I tried adding these vectors together, with the aim of getting a zero vector but I ended up with the following:

$\mathbf{i}(1-1+2) + \mathbf{j}(0+1-1) + \mathbf{k}(-1+2-3) = 2\mathbf{i} - 2\mathbf{k} $

Rather than first informing my tutor about a possible mistake, I am first trying to check whether I am doing something wrong from my side.

Thanks in advance.

Answer 1

Hint: $-(\mathbf{i} - \mathbf{k}) + (-\mathbf{i} + \mathbf{j} + 2\mathbf{k}) + (2\mathbf{i} - \mathbf{j} - 3\mathbf{k}) $ gives you what?