If $\| \mathbf { u } \| = 4$ and $\| \mathbf { v } \| = 6$ ,and the vectors make angles of 140° and 20° with the x-axis respectively,find the component form of the sum of u and v.Round answers to two decimal places.
A) $\langle 2.57,4.62 \rangle$
B)? $\langle - 0.84,5.22 \rangle$
C)? $\langle - 8.7,0.52 \rangle$
D)? $\langle 8.21 , - 1.01 \rangle$
E)? $\langle - 3.07 , - 5.12 \rangle$

Question

Quizplus · Accepted Answer

To find the component form of the sum of vectors $\mathbf{u}$ and $\mathbf{v}$, calculate each vector's components using their magnitudes and angles, then add them. For $\mathbf{u}$, $\langle 4\cos(140^\circ), 4\sin(140^\circ) \rangle \approx \langle -3.06, 2.57 \rangle$. For $\mathbf{v}$, $\langle 6\cos(20^\circ), 6\sin(20^\circ) \rangle \approx \langle 5.64, 2.05 \rangle$. Adding these gives $\langle -3.06 + 5.64, 2.57 + 2.05 \rangle \approx \langle 2.57, 4.62 \rangle$.

If ∥u∥=4\| \mathbf { u } \| = 4∥u∥=4 And ∥v∥=6\| \mathbf { v } \| = 6∥v∥=6

If $\| \mathbf { u } \| = 4$ And $\| \mathbf { v } \| = 6$