Question

Given that P = (-5, 5) and Q = (-13, 6), find the component form and magnitude of 2vector PQ

Answer 1

ANSWER

Component form:

$\binom{ - 16}{2}$

2. Magnitude

$2\sqrt{65}$

EXPLANATION

Given that P = (-5, 5) and Q = (-13, 6),

Vector PQ

$= \binom{ - 13}{6} - \binom{ - 5}{5}$

$= \binom{ - 13 + 5}{6 - 5}$

$= \binom{ - 8}{1}$

2 vector PQ

$= 2 \binom{ - 8}{1}$

$= \binom{ - 16}{2}$

This is the component form.

The magnitude is given by

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

$= \sqrt{ {( - 16)}^{2} + {2}^{2} }$

$= \sqrt{256 + 4}$

$= \sqrt{260}$

$= 2\sqrt{65}$