Notes On Addition of Vectors by Analytical Method - CBSE Class 11 Physics
The accuracy of the results obtained using the graphical method depends on the scale chosen and one’s ability to draw exact parallel lines. The analytical method of vector algebra gives more accurate results.
 
To learn the analytical method of vector algebra, one should  understand the concept of resolution of a given vector along the axes of a rectangular coordinate system using unit vectors for convenience.
 

 
For planar motion or two-dimensional motion the given vector is resolved along  and j only.
 

In three-dimensional space a vector is resolved into three components as shown.To add vectors in three-dimensional space one has to simply add the coefficients of i,  j and k.
 

Summary

The accuracy of the results obtained using the graphical method depends on the scale chosen and one’s ability to draw exact parallel lines. The analytical method of vector algebra gives more accurate results.
 
To learn the analytical method of vector algebra, one should  understand the concept of resolution of a given vector along the axes of a rectangular coordinate system using unit vectors for convenience.
 

 
For planar motion or two-dimensional motion the given vector is resolved along  and j only.
 

In three-dimensional space a vector is resolved into three components as shown.To add vectors in three-dimensional space one has to simply add the coefficients of i,  j and k.
 

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