The unknown vector v satisfies $\displaystyle b \cdot v = \lambda$ and $\displaystyle b \times v = c$ where lambda, b and c are fixed and known.

Find v in terms of lambda, b and c

At first I was thinking of expanding everything out, and so I'd get:

$\displaystyle b_1 v_1 + b_2 v_2 + b_3 v_3 = \lambda$

$\displaystyle b_2 v_3 - v_2 b_3, b_3 v_1 - b_1 v_3, b_1 v_2 - b_2 v_1) = (c_1, c_2, c_3)$

But then that didn't seem to help. Any ideas?