Finding resultant magnitude and resultant vector

[EverT23]

I need help finding out the formulas for finding out the resultant magnitude and the resultant vector. Any help is welcome. Thanks

 

[BiGyElLoWhAt]

How do you add vectors?

Vector A: <1,2,3> OR i + 2j + 3k
Vector B: <2,1,3> OR 2i + j + 3k
A + B = ?

|A| = ?
|B| = ?

|A + B| =?

 

[BiGyElLoWhAt]

One more thing

 

[EverT23]

I don't know How to add them, I have this physics online class that is little to No help on understanding this

 

[BiGyElLoWhAt]

Ok, well let's try something here... I hope I don't get shunned for this lol.

How much do you actually know about vectors? Could you draw me some? View this picture, save it or hit print screen or however you want to get it, open it up in paint and grab yourself the straight line tool.

Can you draw, let's say, the vectors
<1,1>,
<1,2>,
&
<1,3>
?

Take each "tic" as 1 unit.

 

[SteamKing]

I don't know How to add them, I have this physics online class that is little to No help on understanding this

I take it you are completely innocent of trigonometry. You know, Pythagoras and all that.

 

[EverT23]

I tried solving the second, but having tough time with the first one

 

[SteamKing]

I tried solving the second, but having tough time with the first one

The magnitude of the resultant looks OK. How about the angle the resultant makes with the horizontal?

 

[BiGyElLoWhAt]

As for the first, you have a couple right triangles that now share a common side, can you use that side (along with some trig) to make connections between the 2 triangles and ultimately get the side lengths you need?

As steam asked, trig and stuff.
Here's some useful equations (a quick google would give the same results)

$\text{sin}(\theta) = \frac{\text{side opposite of angle in a right triangle}}{\text{hypotenuse of aforementioned right triangle}}$


$\text{cos}(\theta) = \frac{\text{side adjacent to angle (not hypotenuse) in a right triangle}}{\text{hypotenuse of aforementioned right triangle}}$
You can multiply, divide, add, subtract, power, root, or whatever to both sides just like any equality to find a relationship for the particular side you're looking for. Just algebra those e q's and tell them what you want out of them.