Explain how a vector can be resolved into its rectangular components components in two dimension .

Explanation

In a two dimensional Cartesian coordinate system the vector `vec(A) ` is given by
`vec(A) = A_(x) hat(i) + A_(y) hat(j)`
If `vec(A) ` makes an angle `theta` with x - axis, and `A_(x) and A_(y)` are the components of along x-axis and y-axis respectively , then as shown in figure.
`A_(x) = A cos theta, A_(y) = A sin theta`
Where 'A' is the magnitude (length) of the vector `vec(A), A = sqrt(A_(x)^(2) +A_(y)^(2))`