Question

Vector u has a magnitude of 4 with a direction of 50°. Vector v has a magnitude of 6 with
a direction of 25°. Which vector components represent the sum of u + v?

Answer 1

Answer: <8.01, 5.60>.

Step-by-step explanation:

Vector:

$v= (r\cos\theta,r\sin\theta)$

, where r = magnitude and $\theta$ = angle .

As per given,

$u=(4\cos 50^{\circ}, 4\sin 50^{\circ})\\\\\approx(4(0.64),4(0.77))\\\\=(2.56, 3.08)$

$v=(6\cos 25^{\circ}, 6\sin 25^{\circ})\\\\\approx(6(0.91),6(0.42))\\\\=(5.46, 2.52)$

Consider

$u+v=(2.56,3.08)+(5.46,2.52)\\\\=(2.56+5.46,3.08+2.52)\\\\=(8.02,\ 5.60)$

Hence, the correct option is <8.01, 5.60>.