How does resolve a vector into its component? Explain.

Explanation

component of a resolve: In the Cartesian coordinate system any vector `vecA` can be resolved into three components along x, y and z directions. This is shown in figure. Consider a 3-dimensional coordinate system. With respect to this a vector can be written in component form as `vecA = A_x hati + A_y hatj + A_z hatk`
Components of a vector in 2 dimensions and 3 dimensions

Here Ax is the x-component of `vecA` , Ay is the y-component of `vecA` and `A_z` is the z component of `vecA` .
In a 2-dimensional Cartesian coordinate system (which is shown in the figure) the vector A is given by
`vecA = A_x hati + A_z hatj`
If `vecA` makes an angle `theta` with x axis, and `A_x` and `A_y` are the components of `vecA` along x-axis and y-axis respectively, then as shown in figure,

where ‘A’ is the magnitude (length) of the vector `vecA, A = sqrt(A_x^2 + A_y^2)`