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.

 

[Architeuthis Dux]

I can confirm that your solution for finding the resultant and direction of the three given vectors is correct. Your use of trigonometric functions and vector addition principles is appropriate and your final answer of 3.64 for the resultant and -58.5 degrees for the direction is accurate. Keep up the good work!