## Class 11 Physics Online Notes – Introduction to Vector | NCERT Solutions 11th Science

*Physics notes for class 11*: **VECTORS**

The pairs of magnitude and direction are usually called as Vectors. More especially when they follow the vector law of addition. They are represented by an arrow.

*Here A and B are vectors and their resultant are given by A+B by vector *

*Law of addition*.

The direction of the arrow is the direction of the vector, and the length is the magnitude. If the quantity has the only magnitude but has no direction then it is termed as a scalar.

*Watch** and learn vectors and laws of vectors with Class 11th Physics animated videos.*

**LAWS RELATED TO VECTORS**

Addition of vectors

The operation of addition of two vectors can be done by using the law called parallelogram law of vector addition. The addition can be done by taking two vectors as the adjacent sides of a parallelogram by joining their tales and sum can be taken by adding their corresponding components. If A=(x_{1+}x_{2+}x_{3}) and B=(y_{1}+y_{2}+y_{3}).

Then A+B = (x_{1}+y_{1},x_{2}+y_{2},x_{3}+y_{3}).

Watch and understand the concept ‘addition of vectors’, for demos visit *Class 11 Physics* at Takshilalearning.

Multiplication of vectors

For multiplication of two vectors, there are several techniques. Includes

- Cross product: It is the operation which results in a vector that’s why it is also called as the vector product of two vectors. It is taken by the product of their magnitude and sine of the angle between them. Carried out by the formula

A × B = ||A|| ||B|| sin θ n.

Where ‘n’ is unit vector determined by the plane of two vectors.

- Dot product: it is the operation results in scalar of two vectors that’s why it is also called as the scalar product of two vectors. It is taken by product of their magnitude and cosine of the angle between them.

A ⋅ B = ||A|| ||B|| cos θ.

- Triple cross product and multiple products: when three vectors are multiplied then the product are called triple product and if more than three then product is multiple products.

*NCERT Solutions of Class 11th Physics –Vectors are available, for details visit 11th Class Physics. *

**COMPONENTS OF A VECTOR**

The arrow side means the head is the terminal point and tail is the initial point of a vector. The component can be obtained by subtracting the coordinated of terminal point from the coordinate of the initial point

**UNIT VECTOR**:

The vector with magnitude equals to one called as unit vector above vector v can be a unit vector by multiplying its magnitude by1/||v||.

A vector such as <3,4> can also be written as 3<1,0>, 4<0,1>. And that’s why this vector can also be called as special unit vector

Sometimes unit vector can also be called as the direction vector.

*For a detailed explanation of components of Vector click CBSE 11th Class Physics.*

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