A vector A has a magnitude of 5 units and points in the y direction, while a vec

Question

A vector A has a magnitude of 5 units and points in the y direction, while a vector B has three quarters 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)    

(b)    

(c)    

° (counterclockwise from the +x-axis)

Two position vectors,

and

are shown in the diagram below. The green arrow represents vector

while the red one represents

The components of the vectors are as follows:

Explanation / Answer

a) A vector A has a magnitude of 5 units and points in the y direction, while a vector B has three quarter the magnitude of A and points in the +x direction.

Ax = 0
Ay = –5
Bx = (15/4)
By = 0

A+B, add the components.
Rx = 15/4
Ry = –5
R = ((15/4)² + 5²) = 6.25
= arctan (–5/(15/4)) = –53.13º referenced to +x axis. Re your standard, that is +360–53.13 = 306.87º

b) A-B, add the components.
Rx = -15/4
Ry = –5
R = ((15/4)² + 5²) = 6.25
= arctan (–5/(-15/4)) = 53.13º

c) B-A, add the components.
Rx = 15/4
Ry = 5
R = ((15/4)² + 5²) = 6.25
= arctan (5/(15/4)) = 53.13º

d) Ax = -7
Ay = –20
Bx = 15
By = -8

A+B, add the components.
Rx = 8
Ry = –28
R = ((8)² + 28²) =29.12

e) 2A-B, add the components.
Rx =-29
Ry = –32
R = ((29)² + 32²) =43.19

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