SOLUTION: If v = (2, -5), find the magnitude and direction angle of 2v.

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Question 1087028: If v = (2, -5), find the magnitude and direction angle of 2v.
Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
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The magnitude of the vector 2v is sqrt%284%5E2+%2B+%28-10%29%5E2%29 = sqrt%2816+%2B+100%29 = sqrt%28116%29 = 2%2Asqrt%2829%29.


The direction angle of the vector 2v is the same as that of the vector v:

tan%28alpha%29 = %28-5%29%2F2 = -2.5.


Notice that the angle alpha lies in QIV.



Therefore,  alpha = arctan%28-2.5%29,  or, which is the same,  alpha = -arctan%282.5%29.