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# Help With Vectors

## Question

Hello! I'm a first time physics student (soon to be anyways, starting this September). For my summer homework I was tasked with learning about vectors. I am really stumped on adding more than 2 vectors. Anyways, the problem is:

An object travels 20 miles easy, 10 miles south and then 15 miles west.

A. Draw a vector diagram

B. Find the objects displacement

I would really appreciate an explanation for this problem!

## Recommended Posts

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Hi!  First off, let's get you a couple tutorials on vectors and scalars...

Video Tutorial:

Now, to find the displacement, once you have your vectors all lined up tip-to-tail (which they already are), we'll draw a line from the starting point of the first vector to the ending point of the final vector (the dashed purple vector).

To find the magnitude of the displacement, we can use the Pythagorean Theorem.  Draw in black dashed lines are the lengths of the shorter sides of the triangle.

${a^2} + {b^2} = {c^2}$

${(5miles)^2} + {(10miles)^2} = {c^2}$

$125mile{s^2} = {c^2}$

$c = \sqrt {125mile{s^2}} = 11.2miles$

So the final answer would be the displacement is 11.2 miles south east.  If you want, you can find the exact angle of the displacement using your trigonometry formulas.

Hope that gets you started!

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