vector scompsition in two not ortogonal directions

[molossi74]

Does anyone know a formula where :

I have a vector "c" that forms angle "alfa" with "a" direction and angle "beta" :

Does someyone know a formula in order to have vector (c)components on two direction (a e b) known the angles "alfa" e "beta" ?

Thanks
molossi74

 

[JStephen]

If I understand the question, you have one vector and you want to find two vectors in the A and B directions that sum to the original vector?

If that's the case, just lay it out on paper and it becomes a triangle problem. You know all the angles and one side, so Law of Sines should get you the other two sides. If A and B are at right angles, then the original vector is the hypotenuse of a right triangle and it's pretty straightforward.

 

[Denial]

Unless it is a problem in three dimensions!

 

[molossi74]

thanks I have solved it with Carnot theorem !

bye

 

[JStephen]

If two vectors sum to make a third one, they are all in one plane, so it is still a 2-dimensional problem.

 

[Denial]

Correct, of course, JStephen. But the original post (at least as far as I understood it) nowhere talks about two vectors summing to make a third vector. It talks about a vector having components in two (other) directions.