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Find the vector, not with determinants, but by using properties of cross products. k × (i − 4j)?

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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

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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)

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