Vector Addition: Finding Resultant and Direction - Easy Homework Solution

[seizureboi]

Homework Statement

I have three vectors and I need to find the resultant of the three vectors and direction.

Homework Equations

*All angles are with the horizontal

Vector 1 = 18 at an angle of 40 degrees (First Quadrant)
Vector 2 = 10 at an angle of 72 degrees (Second Quandrant)
Vector 3 = 22 at an angle of 55 degrees (Third Quadrant)

The Attempt at a Solution

In the X I got: 18cos(40) - 10cos(72) - 22cos(55) = -1.9
In the Y I got: 18sin(40) + 10 sin(72) - 22sin(55) = 3.1

√(-1.9² + 3.1²) = 3.64 is the resultant

tan^-1(3.1/-1.9) = -58.5 degrees is the direction/angle

I just need confirmation whether this is right or wrong. =)

 

[vela]

Looks good. Well, almost perfect. You should be a little careful with your terminology.

The resultant is a vector, the sum of the three vectors, and it has a magnitude and direction. The 3.64 you found is the magnitude of the resultant, not the resultant itself.

For the direction, you need to be a little careful because arctangent only returns angles between -90 degrees and +90 degrees. You should give a little more information to indicate exactly what the angle is, e.g. which quadrant, measured relative to what, etc.