Explain the resolution of vectors in three dimensional co-ordinates .

Explanation

In the Cartesian coordinate system any vector `vec(A) ` can be resolved into three components along x, y and z direction. This is shown in the figure (b) (Components of a vector in two dimensions and three dimensions).
Consider a 3-dimensional coordinate system. With respect to this a vector can be written in component form as
`vec(A) = A_(x)hat(i) +A_(y)hat(j) +A_(z) hat(k)`
`A = sqrt(A_(x)^(2)+A_(y)^(2)+A_(z)^(2))`