$\langle u + v, w \rangle = \langle u, w \rangle + \langle v, w \rangle$ ; $u = (3, -2), v = (4, 5), w = (-1, 6)$
$\langle u, v \rangle = 4u_1v_1 + 5u_2v_2 $
When I tried to do this I got: $\langle u + v, w \rangle = \langle(48, -50), (-1, 6)\rangle = -348$ (probably the wrong answer)
Looking at it, it appears that:
$\langle u, v \rangle = v_1u_1v_1 + v_2u_2v_2$
but I don't know how to deal with the weighted inner product.