SOLUTION: Two vectors p and q act an angle sixty degrees with each other. If p is 20 unit and q is 8 unit. Find the resultant and its magnitude

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Question 1149366: Two vectors p and q act an angle sixty degrees with each other. If p is 20 unit and q is 8 unit. Find the resultant and its magnitude
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


If we are given only the angle between the two vectors, we can determine the magnitude of the resultant vector; but we have no information that allows us to determine that vector.

For simplicity, let vector p be horizontal, with vector q making an angle of 60 degrees with p. Then the x component of the resultant vector is

20%2B8%2Acos%2860%29+=+20%2B8%281%2F2%29+=+20%2B4+=+24

and the y component is

8%2Asin%2860%29+=+8%2A%28sqrt%283%29%2F2%29+=+4%2Asqrt%283%29

Then the magnitude of the resultant vector, using the Pythagorean Theorem, is

sqrt%28%2824%29%5E2%2B%284%2Asqrt%283%29%29%5E2%29

I leave it to you to do the calculation....