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Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board

18. Cross Product || Vector Product || اردو / हिंदी` || Topic 9.7 | part 3/6

In this video we explained cross product of two vectors also we learn torque as a example and what is right hand rule , what is left hand rule , what is cross product multiplication rule in unit vectors , and component ,
also we learn what is component of cross product ,

and derived the formula for cross multiplication. Unlike cross product, cross product is a Vector quantity and hence it is also called the Vector product. One example is torque

Torque is the twisting force that tends to cause rotation. It is the measure of how much a force acting on an object causes that object to rotate.

also we learn about right hand and left hand rule

The direction of the torque vector is found by convention using the right hand grip rule. If a hand is curled around the axis of rotation with the fingers pointing in the direction of the force, then the torque vector points in the direction of the thumb

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18. Cross Product || Vector Product || اردو / हिंदी` || Topic 9.7 | part 3/6 Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board18. Cross Product || Vector Product...

Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board

17. Dot Product || Scalar Product || اردو / हिंदी` || Topic 9.7 | part 2/6

In this video we explained dot product of two vectors and derived the formula for dot multiplication. Unlike cross product, Dot product is a scalar quantity and hence it is also called the scalar product. One example is work done which is the dot product of force and displacement. The dot product of two vectors is the product of the magnitudes of those vectors and the cosine of the angle between those vectors.
and also explain what is vector projection and what is projection components
also we proof dot product formula
and real meaning of dot product

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17. Dot Product || Scalar Product || اردو / हिंदी` || Topic 9.7 | part 2/6 Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board17. Dot Product || Scalar Product |...

Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board

16. Vector Multiplication || اردو / हिंदी` || Topic 9.7 | part 1/6

In this video we explained vector multiplication and its types. a vector can be multiplied in three ways. One, it can be multiplied by a number; two, it can be multiplied by a scalar and, three, it can be multiplied by a vector. When a vector is multiplied with a vector, there are two ways to do so, one is known as dot multiplication and we get a dot product and the other one is known as cross multiplication and we get a cross product. Dot product is a scalar quantity and a cross product is a vector quantity. When a vector is multiplied with a number it remains the same type of vector with the same direction, but when a vector is multiplied by a scalar the product becomes a different vector with the same direction. In cross product the direction is determined by the right hand rule.

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16. Vector Multiplication || by Scalar || اردو / हिंदी` || Topic 9.7 | part 1/6 Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board16. Vector Multiplication || اردو /...

Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board

14. Vector Addition and Subtraction by Rectangular Component || اردو / हिंदी` || Topic 9.6 | part 2/3

In this video we explained vector addition and subtraction by rectangular component method. When two or more vectors are represented in rectangular unit vector notation, i.e., represented by their components, we have to add the respective components to have the resultant vector.

Or Other Definition

Every single vector can be resolved (broken down) into their component vectors. If we are dealing with a vector in the two dimensional plane, then we can break down the vector into two component vectors, which each lie along one dimension (the x and y axis). Likewise, if we are dealing with a vector in the three dimensional plane, we can resolve that vector into three component vectors. We usually use the xyz plane as the reference frame and begin our vector at the origin. Graphical methods of adding vectors can be very tedious and overall inefficient because they require of the use of protractors and rulers. A much more efficient method of adding or subtracting vectors used in physics and mathematics involves using component vectors. Suppose we want to add up two vectors to find the final resultant vector. First, we must break down each individual vector into its components. Next, we must add up the component vectors that lie along the same axis (for example, add up the all component vectors that lie along the x axis). Then we can use a formula as described in the lecture to find the magnitude as well as the direction of the resultant vector. This method provides us with an accurate and efficient way to determine the resultant vector without having to have to use precision instruments.

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14 Vector Addition and Subtraction by Rectangular Component || اردو / हिंदी` || Topic 9.6 | part 2/3 Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board14. Vector Addition and Subtraction...

Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board

13. Resolution of a Vector into its Components || اردو / हिंदी` || Topic 9.6 | part 1/3

In this video we learn about Resolution of a vector. And what is Vector Components

Resolution of a vector is the splitting of a single vector into two or more vectors in different directions which together produce a similar effect as is produced by a single vector itself. The vectors formed after splitting are called component vectors.

Or Other
DEFINITION

The process of splitting a vector into various parts or components is called "RESOLUTION OF VECTOR"
These parts of a vector may act in different directions and are called "components of vector".
We can resolve a vector into a number of components .Generally there are three components of vector viz.
Component along X-axis called x-component
Component along Y-axis called Y-component
Component along Z-axis called Z-component

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13. Resolution of a Vector into its Components || اردو / हिंदी` || Topic 9.6 | part 1/3 Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board13. Resolution of a Vector into its...

Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board

9. VECTOR ADDITION || Triangle Law & Parallelogram Law | In Hindi | In Urdu | part 2/4 | Topic 9.5

with triangle law and parallelogram law of vector addition. When two vector quantities combine, e.g., when two forces are applied on a point, they create one single vector known as the resultant vector. The process by which we find out the resultant vector is known as vector addition. To perform vector addition we follow two processes, one, triangle law and, second, parallelogram law.

The triangular law of vector addition : If two vectors are represented both in magnitude anddirection by two sides of a triangle taken in same order, then the third side will give the magnitude of the resultant vector with direction in opposite order.

The parallelogram law of vector addition : If two vectors acting simultaneously on a particle are represented in magnitude and direction by the two adjacent sides of a parallelogram drawn from a point, then their resultant is completely represented in magnitude and direction by the diagonal of that parallelogram drawn from that point.

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9. VECTOR ADDITION || Triangle Law || Parallelogram Law | In Hindi | In Urdu | part 2/4 | Topic 9.5 Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board9. VECTOR ADDITION || Triangle Law & Parallel...

Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board

7. Position Vector and its Direction Cosines | In Hindi | In Urdu | part 1/1 | Topic 9.4

In this videos we learn about

In analytic geometry, the direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three positive coordinate axes. Equivalently, they are the contributions of each component of the basis to a unit vector in that direction.

or any of the cosines of the three angles between a directed line in space and the positive direction of the axes of a rectangular Cartesian coordinate system —usually used in plural
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7. Position Vector and its Direction Cosines | In Hindi | In Urdu | part 1/1 | Topic 9.4 Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board7. Position Vector and its Direction Cosines ...

Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board

6. Types of Vectors | In Hindi | In Urdu | part 3/3 | Topic 9.2.3

In this videos we learn about Types Of Vectors

1. Zero Vector or null vector
We define a vector as an object with a length and a direction. However, there is one
important exception to vectors having a direction: the zero vector, i.e., the unique
vector having zero length. With no length, the zero vector is not pointing in any
particular direction, so it has an undefined direction.

2. Unit Vector
A unit vector along any vector is a vector whose direction is the same as the direction of the given vector, but its magnitude is unity. Unit vector along a vector can be achieved by dividing the vector by its magnitude. A unit vector is a fancy name for a direction.

3.Position Vector
Position vector is used to help us find the location of one object relative to another object.
Position vectors usually start at the origin and then terminate at any other arbitrary point.
Thus, these vectors are used to determine the position of a particular point with reference to its origin.

4.Co-Initial Vector
Any given two vectors are called as co-initial vectors if both the given vectors have the same initial point.

5.Coplanar vector
Coplanar vectors are the vectors which lie on the same plane, in a three-dimensional space.
These are vectors which are parallel to the same plane. We can always find in a plane any two random vectors, which are coplanar. Also learn, coplanarity of two lines in a three dimensional space

6.Collinear Vectors. Parallel Vector and Anti-Parallel Vector
Two vectors are said to be collinear, if they act along the same line or along parallel lines.
So these are the necessary conditions. If collinear vectors act in the same direction,
they are known as parallel vectors and if they act in opposite directions, they are known as
antiparallel vectors.

7.Equal Vector
Two vectors are equal if and only if they have the same magnitude in the same direction

8.Netagive Vector
A negative of a vector represents the direction opposite to the reference direction,
It means that the magnitude of two vectors are same but they are opposite in direction

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6. Types of Vectors | In Hindi | In Urdu | part 3/3 | Topic 9.2.3 Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board6. Types of Vectors | In Hindi | In Urdu | pa...

Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board

Unit Vector | In Hindi | In Urdu | part 2/3 | Topic 9.2

In this videos we learn about

what a unit vector is. A unit vector along any vector is a vector whose direction is the same as the direction of the given vector, but its magnitude is unity. Unit vector along a vector can be achieved by dividing the vector by its magnitude. A unit vector is a fancy name for a direction.
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5.Unit Vector | In Hindi | In Urdu | part 2/3 | Topic 9.2 Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh boardUnit Vector | In Hindi | In Urdu | part 2/3 |...

Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board

4. WHAT IS SCALAR AND VECTOR QUANTITY & REPRESENTATION | In Hindi | In Urdu | part 1/3 | Topic 9.2
In this videos we learn about

the concept of a vector quantity. We also discussed about the difference between a scalar quantity and a vector quantity. By definition a vector quantity is a physical quantity with magnitude and direction, whereas, a scalar quantity only has magnitude. For example, displacement, force etc. are vector quantity and distance, mass, time etc. are scalar quantity.

4. WHAT IS SCALAR AND VECTOR QUANTITY & REPRESENTATION | In Hindi | In Urdu | part 1/3 | Topic 9.2 Class 12, Chapter 9: Vectors and 3D Geometry, Sequence of Sindh board4. WHAT IS SCALAR AND VECTOR QUANTITY & REPRE...

Chapter 9: Vectors, Sequence of Sindh board

Cartesian Coordinate System for 3D Space | In Hindi | In Urdu | part 3/3 | Topic 9.1

Aoa in this videos we learn about

Introduction to 3D Geometry, and Cartesian Coordinate System for 3D Space
what is 3D plane , what is right hand rule, what is left hand rule, how to draw point coordinates xyz,
how to find 3d Coordinate in space

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