Vector A has a magnitude of 13 units at a direction of 250 degrees and vector B has a magnitude of 27 units at 330 degrees, both measured with respect to the positive x axis. What is the sum of A and B?

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Vector A has a magnitude of 13 units at a direction of 250 degrees and vector B has a magnitude of 27 units at 330 degrees, both measured with respect to the positive x axis. What is the sum of A and B?

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Answer 1 · 2015-12-29T00:44:06

Convert the vectors to unit vectors , then add ...

Explanation:

Vector A $= 13 [cos 250 i + sin 250 j] = - 4.446 i - 12.216 j$ $=13[cos250i+sin250j]=-4.446i-12.216j$
Vector B $= 27 [cos 330 i + sin 330 j] = 23.383 i - 13.500 j$ $=27[cos330i+sin330j]=23.383i-13.500j$

Vector A + B $= 18.936 i - 25.716 j$ $=18.936i-25.716j$

Magnitude A+B $= \sqrt{{18.936}^{2} + {(- 25.716)}^{2}} = 31.936$ $=sqrt(18.936^2+(-25.716)^2)=31.936$

Vector A+B is in quadrant IV . Find the reference angle ...

Reference Angle $= {tan}^{- 1} (\frac{25.716}{18.936}) = {53.6}^{o}$ $=tan^-1(25.716/18.936)=53.6^o$

Direction of A+B $= 360^{o} - {53.6}^{o} = {306.4}^{o}$ $=360^o-53.6^o=306.4^o$

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Vector A has a magnitude of 13 units at a direction of 250 degrees and vector B has a magnitude of 27 units at 330 degrees, both measured with respect to the positive x axis. What is the sum of A and B?

1 Answer

Explanation:

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