Physics > Basic Vectors > 6.0 Addition of vectors
Basic Vectors
1.0 Introduction
2.0 Representation of vector
3.0 Basic definition related with vectors
3.1 Unit vector
3.2 Negative of a vector
3.3 Modulus of a vector
3.4 Multiplication and division of vectors by scalars
4.0 Types of vectors
4.1 Equal vectors
4.2 Parallel vectors
4.3 Anti-parallel vectors
4.4 Collinear vectors
4.5 Coplanar vectors
4.6 Zero or null vectors
5.0 Angle between the vectors
6.0 Addition of vectors
6.1 Triangle law of vector addition
6.2 Parallelogram law of vector addition
6.3 Relation between triangle and parallelogram law of vector addition
7.0 Subtraction of vectors
8.0 Cartesian co-ordinate system
8.1 Unit vector in cartesian co-ordinate system
8.2 Position vector of a point
8.3 Displacement vector
9.0 Resolving vector into its components
10.0 Dot product of two vectors
10.1 Properties of dot product
10.2 Condition when two vectors are perpendicular
10.3 Angle between two vectors
10.4 Geometrical meaning of scalar product
10.5 Application of dot product
11.0 Cross product of two vectors
6.2 Parallelogram law of vector addition
3.2 Negative of a vector
3.3 Modulus of a vector
3.4 Multiplication and division of vectors by scalars
4.2 Parallel vectors
4.3 Anti-parallel vectors
4.4 Collinear vectors
4.5 Coplanar vectors
4.6 Zero or null vectors
6.2 Parallelogram law of vector addition
6.3 Relation between triangle and parallelogram law of vector addition
8.2 Position vector of a point
8.3 Displacement vector
10.2 Condition when two vectors are perpendicular
10.3 Angle between two vectors
10.4 Geometrical meaning of scalar product
10.5 Application of dot product
When two vectors $\overrightarrow A $ and $\overrightarrow B $ are represented in magnitude and direction by the adjacent sides of a parallelogram, then the resultant $\overrightarrow R$ is given both in magnitude and direction by the diagonal of the parallelogram.
Mathematically,
$$\overrightarrow R = \overrightarrow A + \overrightarrow B $$
$$\left| {\overrightarrow R } \right| = \left| {\overrightarrow A + \overrightarrow B } \right|$$
$\theta:$ angle between the vectors $\overrightarrow A$ and $\overrightarrow B$
$$\tan \alpha = \frac{{B\sin \theta }}{{A + B\cos \theta }}$$
$\alpha: $ angle between the resultant vector and vector $\overrightarrow A$
