Posted by **G0al** on Tuesday, April 30, 2013 at 10:55pm.

I need help:

If vector u has a magnitude of 4 meters and a direction of 17 degrees and vector v has a magnitude of 6 meters and a direction of 133 degrees. Find the magnitude of the resultant vector of u + 3v.

- Trigonometry -
**Reiny**, Wednesday, May 1, 2013 at 8:50am
I made a sketch

labeled end of first trip A, end 2nd trip B to get triangle OAB

OA=4 , AB = 18 and angle BAO = 64° by simple geometry

OA^2 = 18^2+4^2 - 2(4)(8)cos64 , by cosine law

..

OA = 16.6395 m

by sine law: Let angle AOB= Ø

sinØ/18 = sin64/16.6395

...

Ø = 76.5 or 180-76.5

Ø = 76.5 or 103.5

looking at my sketch, I chose 103.5°

so the new direction angle is 103.5+17= 120.5°

Maginitude is 16.6395 m and direction is 120.5°

or

u = (4cos17 , 4sin17)

3v = (18cos133, 18sin133)

u + 3v = (4cos17 , 4sin17) + (18cos133, 18sin133)

= (-8.45 , 14.338)

maginitude = √( (-8.45)^2 , 14.338^2 ) = 16.6395

direction angle

tanØ = 14.338/-8.45

Ø = 120.5°

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