How does resolve a vector into its component? Explain.

1.	How does resolve a vector into its component? Explain.
Answer» Solution :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)`

Discussion