# Finding the direction of the resultant vector of three vectors?

#### HelpMeWIN123

Hi,

I was wondering how one would go about finding the direction of the resultant of three vectors, when performing a vector addition of three vectors. I mean I know how to find the magnitude, by summing all the squares of the component vectors, i and j, and square rooting that sum, but how does one get the direction of that third vector? The whole thing forms a polygon, for god's sake.

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#### yourdadonapogostick

Have you heard of the "Tip to tail method"?

#### HelpMeWIN123

yeah, the only problem is finding the exact direction in degrees using that method is questionable.

#### HelpMeWIN123

For this specific problem I have a motorist drives south at 20.0 m/s for 3.00 min, then turns west and travels at 25 m/s for 2 min, and finally travels northwest at 30. 0 m/s for 1 min. the respective position vectors are -3000 to the west (negative x-axis), -3000 to the south (negative y-axis), and 1800 to the northwest, 45 degrees from the x/y-axes.

#### yourdadonapogostick

Split it into your x and y components. Use your trigonometric funtions to find the direction and use the pythagorean theorem to find the magnitude.

#### HelpMeWIN123

whaaaaaat, that was last week man. These are three main vectors I computed. I already found the magnitude. I just can't find the direction now of these three. The components of the 1800 NW vector you mean? Tail to tip method says -nothing- about components., you have to use your main resultant vectors (the three here) to find the full resultant vector.

#### HelpMeWIN123

Point is, now if i use the tail-tip method, I have a polygon

#### yourdadonapogostick

So, you do want to do it graphically? You can do it both ways. If you are instructed to do it algebraically, do it the way I said. If you are instructed to do it graphically, use tip to tail. If given no specific method, use whichever is more comfortable for you.

It doesn't matter if you have a polygon; You don't have to make a triangle with the vectors. It will still work. If you don't believe me, add two of the vectors and then add that vector to the third.

#### HelpMeWIN123

Alright; I'd much prefer algebraically. Can you outline how I find the direction of the resultant vector of three vectors?

#### yourdadonapogostick

Draw a picture. Two of your vectors should be incredibly easy to break into components since they are due south and due west. You will need to use trig functions to break the other into components(hence the drawing to determine which functions).

Add the components so you have a resultant x component and a resultant y component. To find the magnitude, use the Pythagorean theorem. To find the direction, use the trig functions(again, use the picture).

#### HelpMeWIN123

Dude, listen I did all that. they are incredibly easy to break down into components BECAUSE THEY ARE COMPONENT VECTORS, it's -3000j and -3000i the third vector can be broken down using sin and cosine. MY FIRST POST talked about doing it graphically and that the problem is i didn't know if I SHOULD EYEBALL the direction angle or what. All I'm asking is for an outline of how i should go about discovering the angles exactly, whether it be algebraically or tail to tip.
The 2 resultant angles are 45 degrees. FINE. getting the angles of the resultant of THESE two are my question.
thanks.

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