Finding unknown in a vector cross product

Question

I have a exam question which says

Let a = 2i + 2j + 27k and b = 1i +xj + uk, find the values for x and u if aXb = 0?

Using the cross product rule and treating it like a matrices when determining the determinant I got the answer.

i  j  k

2  2  27

1  x  u

i(2u - 27x) - j(2u - 27) + k(2x - 2)

I am not sure what to do after this step?

Do I set the i, j and k above and solve the equation to 0?

ex.

2u - 27 = 0

2u = 27

u = 27/2

Answer 1

That works. Notice the value of $x$ you get from the $k$ coefficient is consistent with $2u-27x=0$. But the fastest way to solve the original problem notes nonzero vectors have vanishing cross product iff they're parallel, so we need $b=a/2$ to match the $i$ coefficients.