A vector A has a magnitude of 6 units and points in the y direction, while a vec

Question

A vector A has a magnitude of 6 units and points in the y direction, while a vector B has half the magnitude of A and points in the +x direction. What are the magnitude and direction of the following vectors? Give the directions of each as an angle measured counterclockwise from the +x direction. (a) A + B magnitude unit(s) direction ° (counterclockwise from the +x-axis) (b) A B magnitude unit(s) direction ° (counterclockwise from the +x-axis) (c) B A magnitude unit(s) direction ° (counterclockwise from the +x-axis)

Explanation / Answer

A = - 6 j

B = 3 i

(A) A + B = 3i - 6j

magnitude = sqrt(3^2 + 6^2) = 6.7 units

direction = 360 - tan^-1(6/3) = 297 deg  

(B) A - B = - 3 i - 6j

magnitude = 6.7 units

direction = 180 + tan^-1(2) = 243 deg

(C) B - A = 3i + 6j

magnitude = 6.7 units

direction = tan^-1(6/3) = 63 deg

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