Question

If the position vectors of the points A (3, 4), B (5, −6) and C (4, −1) are $\overrightarrow{a,}$ $\overrightarrow{b,}$ $\overrightarrow{c}$respectively, compute $\overrightarrow{a}+2\overrightarrow{b}-3\overrightarrow{c}$.

Answer 1

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are the position vectors of the points $A\left(3,4\right)$, $B\left(5,-6\right)$ and $C\left(4,-1\right)$.
Then,
$\overrightarrow{a}=3\stackrel{⏜}{i}+4\stackrel{⏜}{j}$
$\overrightarrow{b}=5\stackrel{⏜}{i}-6\stackrel{⏜}{j}$
$\overrightarrow{c}=4\stackrel{⏜}{i}-\stackrel{⏜}{j}$
Therefore,
$$\begin{gathered} \overrightarrow{a}+2\overrightarrow{b}-3\overrightarrow{c} \\ =3\stackrel{⏜}{i}+4\stackrel{⏜}{j}+2\left(5\stackrel{⏜}{i}-6\stackrel{⏜}{j}\right)-3\left(4\stackrel{⏜}{i}-\stackrel{⏜}{j}\right) \\ =3\stackrel{⏜}{i}+4\stackrel{⏜}{j}+10\stackrel{⏜}{i}-12\stackrel{⏜}{j}-12\stackrel{⏜}{i}+3\stackrel{⏜}{j} \\ =\stackrel{⏜}{i}-5\stackrel{⏜}{j} \end{gathered}$$