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If 2 vectors are given by 2 consecutive sides of a triangle, then the third side gives:
If we add zero vector (
The unit vector parallel to the resultant vector of
Vector addition is:
Let ABCD be a parallelogram such that
Since each vector may have its own direction, the process of addition of vectors is different from adding two scalars. The most common graphical method for adding two vectors is to place the initial point of the second vector at the terminal point of the first, as in fig (a).
Suppose, for example, that both vectors represent displacement. If an object moves first from the initial point to the terminal point of vector
Parallelogram Law of Addition
A second method for adding vectors is called the parallelogram method. With this method, we place the two vectors so they have the same initial point, and then we draw a parallelogram with the vectors as two adjacent sides, as in fig (b)
Here the sum of the vectors is given by the vector along the diagonal that passes through the common starting point of both the vectors.
Polygon law of addition
If a number of vectors can be represented in magnitude and direction by the sides of a polygon taken in the same order, then their resultant is represented in magnitude and direction by the closing side of the polygon taken in the opposite order.
OR,
Subtraction of Vectors
If a and b are two vectors, then their subtraction or difference
If the vectors are defined in terms of
then their sum is defined as,
If,
then their difference is defined as,
Properties of vector addition
The sum of two vectors is always a vector.
1.
(Commutative property)
2.
(Associative property)
3.
4.
Properties of vector Subtraction
1.
2.
3. For any two vectors
(a)
(b)
(c)
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