Multiplication of vectors ( Dot and Cross product).

In this topic we will discuss about Multiplication of vectors ( Dot and Cross product), and what are the rules of dot (scalar) product and cross(vector) product ?

Before to know about this topic , students must know these topics ,

what is vector quantity? To know click here-

addition of vectors. To know click here-

resolution of vector and rectangular components of a vector . To know click here-

Multiplication of vectors ( Dot and Cross product) –

Scalar product (dot product ) of –

when the product of two vector quantity gives a scalar quantity such kind of product is called scalar product or dot product. The dot product of two vectors  and  is represented by .  ,which is equal to the product of the magnitude of the two vectors  and   and cosine of the smaller angle between them .

Example of dot product –  work done,power , flux .

Vector product ( cross product )-

When the product of two vector quantities gives the vector quantity then such quantity is called vector product. The cross  product of two vectors  and  is represented by x  ,which is equal to the product of the magnitude of the two vectors  and   and sine of the smaller angle between them .the direction of resultant vector is perpendicular to both  and .

Example- Torque , angular velocity,linear velocity , etc.

To download the complete notes of Multiplication of vectors, click here-

Resolution of vectors

In this topic we will discuss about the meaning of resolution of vectors , how can we resolve a vector ? What are the applications of resolution of vectors ? and rectangular components of a vector quantity.

Before to know about the Resolution of vectors , students must know about what is a vector quantity?

To know about the vectors and its notes click here –

After to know about vector quantity , students should learn about addition of vectors.

To know about addition of vectors and its notes ,click here-

Resolution of vectors-

It is the process of splitting a single vector into two or more vectors in different directions which together produce the same effect as is produced by the single vector alone.

Application of resolution of vector –

(1) It is easier to pull a lawn roller than push it –

(2) Walking of a man is the another example of resolution of vector –

Rectangular components of a vector in a plane –

If we split a vector in two component vectors at right angles to each other then the component vectors are called rectangular components of a vector .

To download complete assignment on Resolution of vector click here-

After completing all  the topics related to vectors given above , students has to know about , the next topic related to vector , ADDITION OF VECTORS. To read the notes on multiplication of vectors click here-

ADDITION OF VECTORS

ADDITION OF VECTOR – Vectors can not be added by simple laws of algebra.

Rules of geometric addition of vectors –

• For the addition of two vectors – For the addition of two vectors represent these two vectors by arrowed lines using the same scale . Displace the second vector as its coincide with the head of first vector , then the single vector drawn from the tail of the first vector to the head of the second vector represent their resultant ( addition) vector.

the addition of two vectors can be obtained using Triangle law or parallelogram law of vector addition

• For the addition of three or more vectors – Represent these vectors by arrowed lines using the same scale . Displace these vectors such that the head of the first vector coincide with the tail of the second vector and head of second coincide with the tail of third vector and so on , then the single vector drawn from the tail of the first to the head of the last represent their resultant vector. The addition of three or more vectors can be found using polygon law of vector addition.

Triangle law of vector addition-   It states that if two vectors acting on a particle represented by two sides of a triangle in same order , then the third side in opposite order gives the resultant vector.

TO DOWNLOAD COMPLETE NOTES OF ADDITION OF VECTOR CLICK HERE-ADDITION OF VECTOR

What do you mean by the term vector quantity ?

What do you mean by the term vector quantity? what are the uses of vector quantity? Explain different types of vector.

VECTORS-

Physical quantity having both magnitude and direction called vector quantity . And the physical quantity having magnitude only called scalar quantity . E.X.- suppose a man move 10 km , now in that case I am discussing about  its distance only i.e. it has magnitude only but there is no any information about its direction hence it is a scalar quantity, if we say man  is moving 10 km towards East(or any other direction ) so we can say we are discussing about its displacement i.e. it has both magnitude and direction. A vector quantity is represented as an arrow on its top ex;-  ? ⃗

Vectors can be divided into two ways –

• Polar vector- a vector which has a starting point or a point of application. E. X .- displacement , force etc.
• (ii) Axial vector – Vectors which represent rotational effects and acts along the axis of rotation in accordance with right hand screw rule.

TO DOWNLOAD VECTORS COMPLETE NOTES CLICK HERE.

 Addition of vectors (triangle law and parallelogram of vector addition)