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the magnitude of B⃗ −3A⃗ . Express your answer using three significant figures

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Oct 19th, 2017

You first break each vector into its components. Starting with the positive x axis as 0 degrees and knowing the x and y components are given by the magnitude of each vector multiplied by the cos and sin of each vector's angle respectively we have

Ax = 44*cos(28)

Ay = 44*sin(28)

Bx = 26.5*cos(124)

By = 26.5*sin(124)

The 124 degrees is simply the 180 degrees of the negative x axis minus the 56 degrees shown since we are starting from the positive x axis.

Then we find Bx-3Ax and By-3Ay, which will be the x and y components of B-3A

Bx-3Ax = 26.5cos124 - 3*44*cos(28) = -131.367694

By-3Ay = 26.5*sin(124) - 3*44*sin(28) = -40.00075

To get the magnitude of a vector we express is at the hypotenuse of a right triangle with its x and y components as the 2 other sides and use the Pythagorean Theorem and say m^2 = x^2 + y^2 so

m = ((-131.367694)^2 + (-40.00075)^2)^(1/2) = 137.323 to 3 significant figures.

Sep 20th, 2014

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