Is it possible to decompose a vector into non-perpendicular components?

[physics user1]

Homework Statement

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Homework Equations

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The Attempt at a Solution

When I have to describe a motion I'm supposed to decompose a vector in two directions, for example in an inclined plane is decompose the weight in these directions: the normal to the plane and the parallel to the plane, and that seems logic, but could I decompose the weight in other directions? The same thing for the velocity in a parabolic motion, I decompose the velocity in the vertical and the horizontal directions because it is easier but could I describe the motion using other directions?for example the horizontal and another one inclined with the horizontal by an angle different of 90 ?

I think I could because it's a matter of choice, the motions doesn't change, changes just the way you look at it
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[Herman Trivilino]

You are free to make these choices. Often you can turn a difficult problem into an easy one by a clever choice of coordinate directions.

 

[SammyS]

Homework Statement

2. Homework Equations [/B]

The Attempt at a Solution

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When I have to describe a motion I'm supposed to decompose a vector in two directions, for example in an inclined plane is decompose the weight in these directions: the normal to the plane and the parallel to the plane, and that seems logic, but could I decompose the weight in other directions? The same thing for the velocity in a parabolic motion, I decompose the velocity in the vertical and the horizontal directions because it is easier but could I describe the motion using other directions?for example the horizontal and another one inclined with the horizontal by an angle different of 90° ?

I think I could because it's a matter of choice, the motions doesn't change, changes just the way you look at it

In regard to your last question:

"... for example the horizontal and another one inclined with the horizontal by an angle different of 90° ?"​

You can decompose a vector into two components which are not mutually perpendicular. However, that tends to cause more problems than it solves..