Question

If vector $\overrightarrow{PQ}$ with coordinates of the end points (1, -2) and (4-1) is equal to vector is with coordinates of initial and final points (a, -1) and (0, 0) respectively, then $\left|a\right|=$ ___

Answer 1

Two vectors can be said to be equal if they have the same magnitudes and same directions.
Since $\overrightarrow{PQ}=\overrightarrow{RS}$
So $\left|\overrightarrow{PQ}\right|=\left|\overrightarrow{RS}\right|$
$\left|\overrightarrow{PQ}\right|$ = $\sqrt{(4-1{)}^2+(-1-(-2{\left)\right)}^2}$
= $\sqrt{10}$
Now $\left|\overrightarrow{RS}\right|=\sqrt{(0-a{)}^2+(0-(-1{\left)\right)}^2}$
=$\sqrt{a^2+1}$
So
$\sqrt{a^2+1}=\sqrt{10}$
or a${}^2$ + 1 = 10
a${}^2$ = 9
$\Rightarrow$ a = $\pm$ 3
$\Rightarrow$ $\left|a\right|=3$.