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

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)  $\langle - 3.07 , - 5.12 \rangle$

Quizplus · Accepted Answer

The correct answer is A because the component form of the sum of u and v is $\langle 2.57,4.62 \rangle$. This can be found by using the law of cosines to find the magnitude of the sum of u and v, and then using the angle between the sum of u and v and the x-axis to find the components of the sum of u and v.

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

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