|u|=110, |v|=75, and the angle between u and v (when placed tail to tail is 120 degrees. FInd |u+3v|

Question

Is it 335? Because thats the answer I'm getting

Answer 1

If the angles are placed tail to tail, this is the subtraction of the two vectors. The angle between them is given as 120°. The question is asking for the resultant vector if you multiply the length of v by three then add that to u . If you draw the parallelogram, the angle between the added vectors is 180-120 = 60. So you have a side-angle-side triangle situation, which calls for the cosine law.

|u+3v|² = |u|² + (|3v|)² - 2|u|(|3v|)cos(60°)

= 110² + 225² - 2(110)(225)(1/2)

= 37975

√37975 = 194.872 = |u+3v|