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>.

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>.