Find the vector by using properties of cross products. k\times(i-2j)

Zerrilloh6 2022-01-06 Answered
Find the vector by using properties of cross products.
\(\displaystyle{k}\times{\left({i}-{2}{j}\right)}\)

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jgardner33v4
Answered 2022-01-07 Author has 3902 answers
Remember that the cross product of a vector with itself is 0.
\(\displaystyle{i}\times{j}={k}\)
\(\displaystyle{j}\times{k}={i}\)
\(\displaystyle{k}\times{i}={j}\)
So, the given problem is \(\displaystyle{k}\times{\left({i}-{2}{j}\right)}={k}\times{i}-{2}{k}\times{j}\)
Replace \(\displaystyle-{2}{k}\times{j}\) with \(\displaystyle{2}{j}\times{k}\)
\(\displaystyle={k}\times{i}+{2}{j}\times{k}\)
\(\displaystyle={j}+{2}{i}\)
\(\displaystyle={2}{i}+{j}\)
Thus, we have \(\displaystyle{k}\times{\left({i}-{2}{j}\right)}={2}{i}+{j}\)
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