# Vector Formulas

**Vector Formulas**

A vector can also be defined as an element of a vector space. Vectors are sometimes referred to by the number of coordinates they have, so a 2-dimensional vector is often called a two-vector, an n-dimensional vector is often called an n-vector, and so on.

The important formulas of vectors are given below:

1. The position vector of any point p(x,y) is

or OP = ( x,y ).

2.The magnitude of position vector

and direction

3. The unit vector = where the magnitude of unit vector is 1

Or,the unit vector =

4.The two vectors and are parallel if and where k and m are the scalars.

5.If then is the result vector which is the triangle law of vector addition.

6. The scalar or dot product of any two vectors .

7. The angle between two vectors is

8. and , then :

where

9. If the position vector of A is , position vector of point B is and position vector of mid-point M is m then

10. If the point P divides Ab internally in the ratio m:n then position vector of P is given by which is a section formula.

11.If P divides AB externally in the ratio m:n then

PRODUCT OF TWO VECTORS

1**.Scalar Product ( dot product )**

Let then dot product of & is devoted by read as dot and defined by

**Note:**

if

**OR**

The scalar product of & is devoted by ,

where being angle between &

**Note:1**

**Note:2**

& are perpendicular if =

i.e or

2**.Properties of Scalar Product**

i. .

ii. .

iii.

iv.

v. If then

3.**Vector (cross) Product of two vectors.**

Let be two vectors then the cross product of is devoted by and defined by

=

We can define in terms of determinants as follows

=

**Note:1** being angle between

&

**Note:2 **

**Note:3 ** If , the and & are parallel if .

4. **Properties of cross product**

i.

ii.

iii.

iv.

v. is perpendicular to both and

vi. is a Area of paralelogram with sides and

vii. = area of triangle having , , as position vectors of vertices of a triangle.

Related posts:

- Maths Formulas for Physics Maths Formulas for Physics. List of mathematical formulas used in...
- Vector product ( Multiplying vectors ) Multiplying vectors. Multiplying vectors with scalars , and vectors. Vector...
- Unit Vector Unit Vector. What is unit vector? What are standard unit...
- Components of vectors Components of vectors , components of vectors in two and...
- Adding vectors by components Adding vectors by components. Vector sum by component method....