Question : basic forces again - object on a hill

Hi

I've just been looking at something that says the horizontal component of the force of gravity on a slope = -mg.sin(theta) and the vertical component is -mg cos(theta). Am i being a bit stupid here or is the minus sign because they have included the direction? But then i thought vector components dont have a direction. But then if you are writing a vector in the form
r = ai + bj then a and b can be positive or negative. Does that mean you are giving the components a direction?

thanks

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Answer : basic forces again - object on a hill

>>  But then i thought vector components don't have a direction.

Vector components definitely have a direction.

if you are talking about the 50 deg slope in your picture, gravity would tend to move an object
down (-y direction) and to the left (-x direction).

If your slope was drawn at 130 deg, it would move down (-y) and to the right (+x).