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

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

• Questions are typically answered in as fast as 30 minutes

### Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

jgardner33v4
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 $$\displaystyle{k}\times{\left({i}-{2}{j}\right)}={2}{i}+{j}$$