SOLUTION: Please help me solve this vectors problem: Given vectors of magnitude 3 and 4 with an angle between them of 100°, find the magnitude of the resultant. Thank you in advanced.

Algebra ->  Vectors -> SOLUTION: Please help me solve this vectors problem: Given vectors of magnitude 3 and 4 with an angle between them of 100°, find the magnitude of the resultant. Thank you in advanced.      Log On


   

Question 980592: Please help me solve this vectors problem:
Given vectors of magnitude 3 and 4 with an angle between them of 100°, find the magnitude of the resultant.
Thank you in advanced.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Draw the vectors where the tails are at the same point. The vectors are shown in blue. The resultant vector is shown in red.


Also, add in auxiliary lines to form a parallelogram. These are the black dashed lines.


Because we have a parallelogram, the adjacent angles are supplementary. So 100+x = 180 means x = 80 degrees. Also, the opposite sides of any parallelogram are congruent. All of this is shown below in the drawing.





The goal is to find the length of the red vector. To do this, we use the law of cosines c%5E2+=+a%5E2+%2B+b%5E2+-+2%2Aa%2Ab%2Acos%28C%29


In this case, the sides of the triangle are a+=+3, b+=+4, and 'c' is unknown. Angle C is 80 degrees. Solve for c to get...


c%5E2+=+a%5E2+%2B+b%5E2+-+2%2Aa%2Ab%2Acos%28C%29


c%5E2+=+3%5E2+%2B+4%5E2+-+2%2A3%2A4%2Acos%2880%29


c%5E2+=+9+%2B+16+-+24%2Acos%2880%29


c%5E2+=+25+-+24%2Acos%2880%29


c%5E2+=+25+-+24%2A0.173648


c%5E2+=+25+-+4.167552


c%5E2+=+20.832448


sqrt%28c%5E2%29+=+sqrt%2820.832448%29


c+=+4.564258


The magnitude of the resultant is approximately 4.564258 units long.