Question

If $\overline{a}=\hat{i}+\hat{j}-2\hat{k},\overline{b}=2\hat{i}-\hat{j}+\hat{k}$ and $\overline{c}=3\hat{i}-\hat{k}$ then, find the scalars $m$ and $n$ such that $\overline{c}=m\overline{a}+n\overline{b}$.

Answer 1

$3\overline{i}-\overline{k}=m(\overline{i}+\overline{j}-2\overline{k})+n(2\overline{i}-\overline{j}+\overline{k})$)

So we get an comparison,

$m+2n=3m-n=0$

and $-2m+n=-1$

on using first two and solving, we get $m=n=1$

and since this satisfies $-2m+n=-1$

we can say that $m=n=1.$