Physics > Basic Vectors > 3.0 Basic definition related with 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
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
4.2 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
A unit vector is a vector of unit magnitude drawn in the direction of a given vector.
In other words, unit vector gives the direction of a vector.
Unit vector is represented as $\widehat A$.
We call it as $A$ cap or $A$ hat.
As we know vector is mathematically represented as,
$$\overrightarrow A = \left| {\overrightarrow A } \right|\widehat A$$ or $$\widehat A = \frac{{\overrightarrow A }}{{\left| {\overrightarrow A } \right|}} = \frac{{\overrightarrow A }}{A}$$
So, unit vector or direction for any vector is found by dividing the given vector by its magnitude.
Note:
- The magnitude of a unit vector is unity i.e. $1$.
- A unit vector has no units.
- It gives the direction of a vector.
- $\widehat i$, $\widehat j$ and $\widehat k$ are the unit vectors along $x$, $y$ and $z$ axis respectively.
So, vector $\overrightarrow {OP} $ can be written as,
$$\overrightarrow {OP} = a\widehat i + b\widehat j + c\widehat k$$
$a,b$ and $c$ is the magnitude along $x,y$ and $z$ respectively.
