Recall the definition of the cross product:
i x i = j x j = k x k = 0
i x j = k
j x k = i
k x i = j
The cross product is antisymmetric, or anticommutative, meaning that for any vectors u and v, we have u x v = - (v x u).
It's also distributive, so for any vectors u, v, and w, we have (u + v) x w = (u x w) + (v x w).
Taking all of these properties together, we get
b x a = (6i - j + 2k) x (2i + 2j - 5k)
b x a = 12 (i x i) - 2 (j x i) + 4 (k x i)
............. + 12 (i x j) - 2 (j x j) + 4 (k x j)
............. - 30 (i x k) + 5 (j x k) - 10 (k x k)
b x a = 1 (j x k) + 34 (k x i) + 14 (i x j)
b x a = i + 34j + 14k
