Vectors, Condition of Maxima and Minima

Use of Vector Algebra
The addition of two vector quantities can be described by triangle law and parallelogram law. If the number of vectors are more than two, the addition is done by the polygon law of vector addition.

Triangle Law:



Parallelogram Law:



Polygon Law:





If the vectors a, b, c and d are arranged in same order such that the polygon is closed i.e. there is no space for R, then |R| = 0. Thus the polygon law can be used too show the zero resultant. "If the given vectors can be represented by the sides of a closed polygon when taken in same order, then their resultant is zero."

Addition and Subtraction:
When vectors are given in terms of rectangular components, their addition and subtraction can be made as per the given example

Example:
Two forcesact on a body. Find the net force on the body and its direction with x-axis.

Solution:



Concept of Maxima and Minima

If y = f(x), then

y is maximum or minimum for a value of x, obtained from the condition= 0

If< 0, then y is maximum

and If> 0, then y is minimum.