Find the vector, not with determinants, but by using properties of cross products. k × (i − 4j)?
we know that
i x j = k,
j x k = i,
k x i = j.
Also we know anticommutativity of the cross product:
a x b = – b x a
Then k x i – 4 k x j = j + 4i
Look at the image in link first.
k × (i − 4j)
= k x i – k x 4j
= k x i – 4(k x j)
= j – 4(-i)
= j + 4i
(which we normally wrte as 4i + j)