Question

Part A

Answer 1

Answer:

$^{\to}_{PQ}+4^{\to}_{RS}=\:$

$|^{\to}_{PQ}+4^{\to}_{RS}|=7\sqrt{13}$

Step-by-step explanation:

The given points have coordinates; P=(5,4), Q=(7,3), R=(8,6), and S=(4,1).

$^{\to}_{PQ}=^{\to}_{OQ}-^{\to}_{OP}$

$^{\to}_{PQ}=\:-\:$

$^{\to}_{PQ}=\:$

$^{\to}_{PQ}=\:$

$^{\to}_{RS}=^{\to}_{OS}-^{\to}_{OR}$

$^{\to}_{RS}=\:-\:$

$^{\to}_{RS}=\:$

$^{\to}_{RS}=\:$

$^{\to}_{PQ}+4^{\to}_{RS}=\:+4\:\:$

$^{\to}_{PQ}+4^{\to}_{RS}=\:+\:\:$

$^{\to}_{PQ}+4^{\to}_{RS}=\:$

$^{\to}_{PQ}+4^{\to}_{RS}=\:$

The correct answer is C

The magnitude is given by:

$|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{x^2+y^2}$

$|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{(-14)^2+(-21)^2}$

$|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{196+441}$

$|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{637}$

$|^{\to}_{PQ}+4^{\to}_{RS}|=7\sqrt{13}$

The correct answer is B