addition of vectors

[papernuke]

how do you add vectors that arent either going in the same direction or the exact opposite?

ex. how do you add two vectors with a 35 degree angle (when attached)

i remember (from my classes) that you make a triange or something.. but then what?

[zero]

It's like following the directions of a pirate's treasure map.

Vector addition is nothing more than following one vector (walk east for 50 paces) and then following the other (walk west by northwest for 12 paces). On the cartesian plane it doesn't even matter which you do first, as there are no quicksand pits to avoid.

[Keiji]

how do you add vectors that arent either going in the same direction or the exact opposite?

ex. how do you add two vectors with a 35 degree angle (when attached)

i remember (from my classes) that you make a triange or something.. but then what?

resolve components and add up.

(2i+j) + (j-5i) = 2j-3i, for example.

[Nick]

OK, here's how it goes:

To add 2 or more vectors, make a data chart. In this chart R is the magnitude and 0 (represents theta) is the angle in degrees.

.............R * Sin0 | R * Cos0
.............-----------------------
Vector 1 | |
Vector 2 | |
Vector 3 | |
...

After you fill that in, take the sum of all the sin values and the sum of all the cosine values. The sum of all the sin values is the total Y force (upward/downward) and the sum of all the cos values is the total X force (left/right). So, if you draw a vector of zero degrees with a magnitude of X, and attach it head-to-tail with a vector of ninety degrees with a magnitude of Y, you get a right triangle with the Resultant vector as the hypotenuse. So use Pythagorean theorem and your set!

This is assuming your adding like-vectors. So adding a velocity vector and another velocity vector is OK, but adding velocity with gravity (a force) won't work. Sorry

[papernuke]

It's like following the directions of a pirate's treasure map.

Vector addition is nothing more than following one vector (walk east for 50 paces) and then following the other (walk west by northwest for 12 paces). On the cartesian plane it doesn't even matter which you do first, as there are no quicksand pits to avoid

-zero

...i said NOT just opposite or same direction..

resolve components and add up.

(2i+j) + (j-5i) = 2j-3i, for example.

-Hayate

how do you resolve the components? and is that the only equation you can use? or isnt there a way where you make a triange and square/cube some things..

[Keiji]

It's like following the directions of a pirate's treasure map.

Vector addition is nothing more than following one vector (walk east for 50 paces) and then following the other (walk west by northwest for 12 paces). On the cartesian plane it doesn't even matter which you do first, as there are no quicksand pits to avoid

-zero

...i said NOT just opposite or same direction..

bearings of 090 (east) and 315 (west northwest) are not "just opposite or same direction".

resolve components and add up.

(2i+j) + (j-5i) = 2j-3i, for example.

-Hayate

how do you resolve the components? and is that the only equation you can use? or isnt there a way where you make a triange and square/cube some things..

A vector with length r and angle θ is, in component form, rcosθi + rsinθj.

[papernuke]

It's like following the directions of a pirate's treasure map.

Vector addition is nothing more than following one vector (walk east for 50 paces) and then following the other (walk west by northwest for 12 paces). On the cartesian plane it doesn't even matter which you do first, as there are no quicksand pits to avoid

-zero

...i said NOT just opposite or same direction..

bearings of 090 (east) and 315 (west northwest) are not "just opposite or same direction".

I thought it was only west. sorry.

resolve components and add up.

(2i+j) + (j-5i) = 2j-3i, for example.

-Hayate

how do you resolve the components? and is that the only equation you can use? or isnt there a way where you make a triange and square/cube some things..

A vector with length r and angle θ is, in component form, rcosθi + rsinθj.

In the last part, what is the "i" in both of them?

[Keiji]

http://en.wikipedia.org/wiki/Unit_vector

[Nick]

resolve components and add up.

(2i+j) + (j-5i) = 2j-3i, for example.

-Hayate
how do you resolve the components? and is that the only equation you can use? or isnt there a way where you make a triange and square/cube some things..

A vector with length r and angle θ is, in component form, rcosθi + rsinθj.

I feel ignored

[papernuke]

I feel ignored

-Nick
Its not that you're being ignored.. but its just that Hayate's explanations are easier. .. not that much easier though..