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components of vectors: am i over complecating it?

components of vectors/ resolving vectors is pretty straight forward ik but I just read something im my text book (for the spec ) and we didn't do it in class and I don't get it at all
here it is :
"sometimes sit is useful to find the components in directions other than horizontal and vertical. eg. for the forces on a car on a slope the sensible directions to calculate components of the forces or velocity are parallel to and at right angle to the slop.
the important thing to remember is that the component of a vector,A, in a direction at angle theta to the direstion of the vectoe is always Acostheta "
there are diagrams as well but I cant put them on
1) 'A' arrow is going diagonal up towards the right and the vector Is going horizontal to the right and theta is in between them
there are two more diagrams, its just the same one rotated
can someone pls explain this to this to me ik its simple but I just want a straight forward and simple explaination that will go in my head.

thanks
Reply 1
Avatar for Pangol
Pangol
15
If you have a problem such as a car going up a slope, you can usually solve all of the problems you will be set just by resolving horizontally and vertically, as you usually do. But this can be quite awkward to actually do. It is often easier to resolve parallel to the slope and perpendicular to the slope, so you are still resolving in two perpendicular directions, just not horizontally and vertically any more. It will probably be easier to see this if you simply turn the page containing the problem around, so that the direction of "parallel to the slope" looks horizontal to you.

You can do this with any two perpendicular directions. A careful choice of directions to resolve can make some problems much easier, especially if you have two unknown forces which are perpendicular to each other (resolve in the direction of one of them, and the other has no component in that direction).

(The two directions don't even have to be perpendicular to each other, so long as they are not parallel, but that is unlikely to make any A Level problems easier!)
Reply 2
Avatar for Arbolus
Arbolus
13
Original post by Exotic-L
components of vectors/ resolving vectors is pretty straight forward ik but I just read something im my text book (for the spec ) and we didn't do it in class and I don't get it at all
here it is :
"sometimes sit is useful to find the components in directions other than horizontal and vertical. eg. for the forces on a car on a slope the sensible directions to calculate components of the forces or velocity are parallel to and at right angle to the slop.
the important thing to remember is that the component of a vector,A, in a direction at angle theta to the direstion of the vectoe is always Acostheta "
there are diagrams as well but I cant put them on
1) 'A' arrow is going diagonal up towards the right and the vector Is going horizontal to the right and theta is in between them
there are two more diagrams, its just the same one rotated
can someone pls explain this to this to me ik its simple but I just want a straight forward and simple explaination that will go in my head.

thanks


Essentially, it doesn't matter what direction the basis vectors in a vector space point, so long as they're orthogonal to one another. You could have the basis pointing horizontally and vertically, or you could have them pointing at an angle θ below the horizontal and θ to the left of the vertical. Any vector which can be described by the first set can also be described by the second set. You can use trigonometry to convert between the two.

The following diagram might help:

20160217_195147.jpg

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