Question

v of magnitude 100 and direction 172 degrees, and w of magnitude 300 and direction 310 degrees, find v+w

Answer 1

From the attached diagram, we can see that the vector v and vector w form a triangle with an angle of 310-172=138 degrees

Since the vector v+w is the opposite of angle 138 degrees, we can use cosine rule to find the size of vector v+w


`(v+w)^(2) = v^(2) + w^(2) - 2(v)(w) cos(138)`


`(v+w)^(2) = 136939.6885`


`v+w = √(136939.6885)`


`v+w = 370.1 (to one dp)`