Question

Given that P = (5, 9) and Q = (13, 12), find the component form and magnitude of vector PQ.

Answer 1

$\bf \begin{cases} P=(5,9)\\ Q=(13,12) \end{cases}\qquad\stackrel{\vec{PQ}}{\ \textless \ 13-5~~,~~12-9\ \textgreater \ }\implies \ \textless \ 8~,~3\ \textgreater$

Answer 2

ANSWER

The vector in the component form is

$\binom{8}{3}$
and the magnitude is

$\sqrt{73}$


EXPLANATION

The given points are P=(5,9) and Q=(13,12).


We want to find the component form of vector PQ.

Let the components of vector PQ be

$\binom{x}{y}$

Vector PQ can express in terms of position vectors as follows:




This implies that;


$\binom{x}{y} =\binom{13}{12} - \binom{5}{9}$

We subtract the corresponding components to get;

$\binom{x}{y} = \binom{13 - 5}{12 - 9}$
The vector in component form is

$\binom{x}{y} = \binom{8}{3}$



The magnitude of vector PQ is

$= \sqrt{ {x}^{2} + {y}^{2} }$



$= \sqrt{ {8}^{2} + {3}^{2} }$


$= \sqrt{64+ 9}$




$= \sqrt{73}$