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# 1.1 Scalar and Vectors

## (a) define the terms scalar and vector.(b) determine the resultant of two vectors by a graphical method.(c) list the vectors and scalars from distance, displacement, length, speed, velocity, time, acceleration, mass and force.

The terms Scalar & Vector are used to differentiate Physical Quantities. What are Physical Quantities?

Physical Quantity:  Any thing that can be measured is called a Physical Quantity For example

Speed, Momentum, Moment, Velocity, Acceleration, mass, volume, area, distance, speed, density, pressure, Energy, work done, temperature, heat,  Weight, Displacement,light and all forms of energies, current, voltage Force and all types of forces ie Friction, Upthrust, Drag etc.

Defination of Scalar Quantity: Such a Physical Quantity that can be specified by magnitude or value (number) only. For example, when you ask someone for time, mass, volume or distance they would only tell a number(magnitude) say its 120 clock, I am 65 kg, 2 liters of petrol and you understand exactly what is means. So you can understand some Physical quantities by their numbers only.

Note: The term magnitude means number or value of something for example 5 kg is the value of mass of something or 100 km/h is the magnitude of speed.

Definition of Vector Quantity: Such a Physical Quantity that need magnitude and direction for their specification. For example, when you are applying force you must mention: how much force you are applying and in which direction. Similarly, acceleration, velocity etc requires magnitude and direction for their complete specifiation.

Pilots while flying air-craft requires speed and the direction in which they are moving. If direction is not specified to them they would disappear somewhere else.

Representation of Vector: So vectors require number & direction for their specification. That is why vectors are represented by arrow or graphically. The size of arrow is the magnitude of the vector. Operations on Vector Quantities:

The mathemataical operations (+, -, x & /) on vector quantities are different than normal operations on numbers. Vector Algebra is different-- don't be afraid we will deal with abnormally easy vectors addition, subtraction, multiplication and division. In Vector's addition 2 + 2 does not necessarily means 4 or 4-2 does not necessarily means 2. Therefore, vector quantities are treated bit different.

Why vector's addition, subtraction, multiplication and division is bit different than normal numbers? This is because they have directions. If one vector is acting in different direction than another, therefore, their addition and subtraction can not yeild same results. For example, the velocity of one plane is north side and other is south side so directions are opposite, therefore, results would be different than if they were moving in same direction.

Also, vectors can be positive (+) and negative (-) while scalars can only be of positive values.

The only difference between +ve and -ve vectors is that of only direction. -ve vector would have opposite direction to that of +ve vector.

As mentioned earlier, vector addition & subtraction is not as same as Year-6 or graduation level addition & subtraction of numbers. It's a totally different ball game.

Is there any condition in which vector addition & subtraction can be normal?

Yes, when vectors are acting in same direction (angle). In such condition 2 + 2 = 4 and 10 - 8 = 2. The chart given below can further clearify your idea.

Vector Addition & Subtraction in same direction:

• If forces are acting in same direction they would add.
• If forces are acting in opposite direction they would subtract. The force which is the result of two or more forces is called resultant force. In first example, 10 N is the resultant force of 5 N and 5 N acting in same direction.

Similarly, 0 N is the resultant force of two forces acting in opposite direction 5 N and -5 N.

In last example, 10 N is acting upwards and -5 N acting in opposite direction the resultant force would be 5 N upwards.

Note: Addition of force is a simple mathematical operation, you just need to see in which direction forces are acting and associated signs--all you then need to do is to some do grade 2 maths.

Vector Addition & Subraction in different direction:

## Vector Multiplication:

Multiplication of two vectors is not a part of the course. However, multiplication of vectors by numbers is in syllabus.

## Multiplication of vectors with numbers:  ## Vectors' Division: Vector Quantities: momentum, moment, force and all types of forces ie friction, upthrust, drag etc, velocity, acceleration, weight, displacement.

Scalar Quantities: mass, volume, area, distance, speed, density, pressure, Energy, work done, temperature, heat, light and all forms of energies, current, voltage, etc.

## appreciate the vector nature of a force

Since force is a vector quantity and all vectors are represented by arrows. Therefore, force is represented by arrows.

If in one direction, force is positive than in other direction it would be negative. As shown below for 1 N For example, weight is always shown with direction downwards(to the center of Earth). Friction with direction opposite to the direction of motion. Push direction inwards to an object and pull direction is outwards. In above two examples, forces are shown with arrows and that is the only way to represent these forces. In first diagram, the person is pushing an object with a force Fa while the weight of the object is Fg and FN Which is the normal reaction from the ground.