Vector has a magnitude of 8.10 units and makes an angle of 52.0° with the positive x-axis. Vector also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods find the following.

Question

Vector  has a magnitude of 8.10 units and makes an angle of 52.0° with the positive x-axis. Vector  also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods find the following.
     a) The vector sum 
Magnitude of A + B:___ units
Direction of A + B ____° counterclockwise from +x-axis
(b) The vector difference A - B.
Magnitude of A - B______  units
Direction of A -B_______° counterclockwise from +x-axis

Henry · Answer

a. 8.1[52o] + 8[180o]

X = 8.1*cos52 + 8*cos180 = 4.99 Units
Y = 8.1*sin52 + 8*sin180 = 6.38 Units.

Mag. = Sqrt(4.99^2+6.38^2 = 8.1 Units

tanA = Y/X = 6.38/4.99 = 1.27856
A = 51.97o = Direction.

b. 8.1[52o] - 8[180o]
Subtract and use same procedure as "a".