Question

A vector A has a magnitude of 4 units and points in the -y-direction, while a vector B has one quarter 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) ° (counterclockwise from the +x-axis) direction (b) A B magnitude unit(s) (counterclockwise from the +x-axis) direction o (c) B - A magnitude unit(s) ° (counterclockwise from the +x-axis) direction

Answer 1

The vector Ais, Ā=4(-3) The vector B is, B =1(i) a) A+B=4(-1)+1(i) =ị -4j Its magnitude is, 12 +(-4) = V17 = 4.1 Direction is, 4 = tan = -1 4 = 1 = -76° Thus it is at an angle of 284° counter clock wise from positive x axis.

b) A-B=4(-j)+1(i) =-i-4j Its magnitude is, = (–11° +(-4) = V17 Direction is, = 4.1 4 =tan - 1 = = 76° Thus it is at an angle of 256° counter clock wise from positive x axis.

c) B-A=1(i)-4(-i) =i +4j Its magnitude is, = V12+(4)? 17 = 4.1 Direction is, = 4 O=tan - = 76° Thus it is at an angle of 76° counter clock wise from positive x axis.