Vector Subtraction and Resolution of a Vector

Vector Subtraction

Given vectors A and B as follows:



The parallelogram for vector subtraction takes the following form:





Resolution of a Vector

A vector may be resolved into to components having known lines of action using the parallelogram law:

Given the vector R below:



Extend parallel lines from the head of vector R to form components in a and b axis



The resolution of vector R into vector A and vector B is as follows:

Multiplication and Division of a Vector by a Scalar

The diagram below shows that when a vector is multiplied by a scalar, its magnitude changes but not its direction.  For example if vector A is multiplied by 2, its magnitude is doubled (i.e. length of the arrow doubles).  The same concept applies to the division of vectors.

Force Vectors - Scalars and Vectors

 

Scalars and Vector Table of Comparison