A bit stuck on part (ii) of this question:
OABC is a rectangle. With respect to the origin, O, the position vectors of $\mathbf{a}$ and $\mathbf{b}$ are $2\mathbf{i} - 3\mathbf{j} + 5\mathbf{k}$ and $s\mathbf{i} + 3\mathbf{j} + 7\mathbf{k}$ respectively.
(i) Find the value of s.
(ii) Find vector equations for the diagonals of AC and OB.
Part (i) was all good, $s = 6$.
For part (ii), I got that the vector equation for OB is $t(6 \mathbf{i} + 3 \mathbf{j} + 7 \mathbf{k})$ but I'm not sure what the vector equation for AC is.
I realize it's got to satisfy $\vec{OC}\cdot\vec{OA} = 0$ and $\vec{BC}\cdot\vec{AB} = 0$ and thus I have the equations:
$$2x - 3y + 5z = 0$$ $$2x + 3y + z - 28 = 0$$
However with 3 unknowns and 2 equations I seem to be missing something. Any help would much appreciated, thanks!
Hint
$\vec{OC}+\vec{OA}=\vec{OB}$