A vector has an #x# component of -25.0 units and a #y# component of 40.0 units. What is the magnitude and direction of this vector?

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Answer 1 · 2017-01-18T22:34:34

The magnitude is #~~ 47.17#
The angle is #~~ 2.13# radians

To compute the magnitude, use:

#|v| = sqrt(x^2 + y^2)#

#|v| = sqrt((-25)^2 + 40^2)#

#|v| ~~ 47.17#

The signs of x and y indicate that the direction angle is in the second quadrant, therefore, use:

#theta = pi + tan^-1(y/x)#

#theta = pi + tan^-1(40/-25)#

#theta ~~ 2.13# radians