Understanding Vector Addition: Pythagorean Method vs. Direct Addition Explained

[MoreZitiPlease]

I need help with adding vectors. I basically want to know when do I use the pythagorean method and when do I simply add them.

Please.

This has me confused.

 

[MoreZitiPlease]

please. :(

 

[salman213]

(1,1,1) + (1,1,1) = (2,2,2)

magnitude of the vector is equal to

square root of 2^2 + 2^2 + 2^2 = root pf 12

 

[MoreZitiPlease]

what?

I mean if its 8m N + 6 M E [example]

should I do the theorem or no?

 

[cristo]

what?

I mean if its 8m N + 6 M E [example]

should I do the theorem or no?

Draw a diagram. You will see that those vectors form two sides of a right angled triangle, of which the hypotenuse is the resultant.

 

[MoreZitiPlease]

so if they are on a different axis: phythagorean thereom?
same axis: add?

 

[salman213]

if they are collinear then add them otherwise if the vectors are perpendicular (ie - 1 is North and the other is East) then you use the pythagorean thereom to find the resultant

 

[cristo]

so if they are on a different axis: phythagorean thereom?
same axis: add?

To get the magnitudes then, yes, if two vectors point in the same direction you can add them to get the resultant. If not, it is always safer to draw a diagram.

Note that, however, if you want to simply add vectors, you can do it component-wise; so if a=(x,y), b=(u,v), then a+b=(x+u,y+v).

 

[rock.freak667]

If the angle between them is 0 or 180, you add or subtract as necessary...if the angle is 90 degrees...the hypotenuse is the resultant

if the angle is any other obtuse angle...you use the parallelogram law