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## Homework Statement

Three vectors, A, B and C each have a magnitude of 50 units. Their

directions relative to the positive direction of the x-axis are 20°, 160° and

270°, respectively. Calculate the magnitude and direction of each of the

following vectors.

1.) A + B + C

2.) A-B+C

3.) 2(A+C)

## Homework Equations

a^2 + B^2=C^2

## The Attempt at a Solution

1.)

Vector A

Ax=50cos20=46.985

Ay=50sin20=17.101

Vector B

-Bx=50cos20=-46.985

By=50sin20=17.101

Vector C

Cx=0

Cy=-50

Ax+Bx+Cx=46.985+(-46.985)+0=0

Ay+By+Cy=17.101+17.101+(-50)=-15.798

0^2 +(-15.798)^2=c^2

c=15.798

tan^-1= 0 degrees

2.

Ax-Bx+Cx=46.985+(--(makes positive) 46.985) + 0=93.97

Ay-By+Cy=17.101+(-17.101)+(-50)=-50

(-50)^2+(93.97)^2=106.444

tan^-1=-50/93.97=28.02 degrees below x axis

3.

2(Ax+Cx)=2(46.985+0)=93.97

2(Ay+Cy)=2(17.101+(-50))=-65.798

(-65.798)^2+(93.97)^2=c^2

C=114.72

tan^-1(-65.798/93.97)

=35.0 degrees below x axis

Did I do this correct?