Question

Consider vector u which has magnitude 35 at 25° and vector v which has magnitude 50 at 120°. Find the component form of the resultant vector u + v

Answer 1

Answer on Question #76908 – Math – Geometry

Question

Given:

$$|u| = 35; \quad \text{alpha} = 25{}^\circ;$$ $$|v| = 50; \quad \text{beta} = 120{}^\circ.$$

Find $u + v$

Solution

Component form vectors $u, v$

$$u = \langle |u| * \cos(\text{alpha}); |u| * \sin(\text{alpha}) \rangle$$ $$v = \langle |v| * \cos(\text{beta}); |v| * \sin(\text{beta}) \rangle$$

Component form of the resultant vector:

$$u + v = \langle |u| * \cos(\text{alpha}) + |v| * \cos(\text{beta}); |u| * \sin(\text{alpha}) + |v| * \sin(\text{beta}) \rangle$$ $$u + v = \langle 35 * \cos(25{}^\circ) + 50 * \cos(120{}^\circ); \quad 35 * \sin(25{}^\circ) + 50 * \sin(120{}^\circ) \rangle$$ $$u + v = \langle 6.72; 58.09 \rangle$$

Answer: $\langle 6.72; 58.09 \rangle$

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