Three vectors a, b, and c each have a magnitude of 50m and lie in the x-y plane. their directions relative to the positive x-axis are 30 degrees, 195 degrees, and 315 degrees, respectively. what are (a) the magnitude and (b) the angle of the vector a + b + c, and (c) the magnitude and (d) the angle of a-b+c? what are the (e) magnitude and (f) angle of the fourth vector d such that (a+b)

a)

b) Θ=º

c)

d) β=º

e)

f) ∅=º

Explanation:

First of all, we need to establish our vectors and it's directions:

A=50 m, 30º

B=50 m, 195º

C=50 m, 315º

Now that we have the three vectors, we need to calculate the x and y components:

Now, that we have the components, we can calculate the resultant's components:

To find the resultant of the vector A+B+C we need to do the following steps:

a)

To find the angle it's necessary to use :

b) Θ=º

To find the resultant of the vector A-B+C we need to do the following steps:

c)

To find the angle it's necessary to use :

d) β=º

To find D=A+B it's important to follow the following steps:

e)

f) ∅=º