Vector Calculus
SCALAR Vs VECTOR
Physical quantity:
- Any physical property that can be measured and represented by a number.
- For example, temperature, area, speed, etc.,
...measuring How tall is he?? is a physical quantity but measuring how smart is he?? is not a physical quantity…
Scalar vs Vector:
Scenario $1$
Teacher asks a student, “What is your $10^{th}$ mark??”
What will be her answer??
It will be like… “It’s 490 madam…”
For the question, What is your tenth mark? Just answering with a number $(490)$ is enough.. Right??
🌾From this, we can say some questions can be answered just with a number.
What is the length of this bridge?
What is the temperature of this room?
What is the area of this land?, etc.,
🌾Quantities like length, temperature, area, volume, speed, etc., can be defined just with a number (magnitude only).
Quantity that can be defined with its magnitude only is termed as a SCALAR.
Scalar = magnitude only
Scenario $2$
Teacher asks a student to bring her a piece of chalk from the staff room.
Student: Sorry Mam… I’m new to this school. I don’t know where the staffroom is..
Teacher: It is $10$ feet away from this classroom.
When the student enters the corridor, there are two ways in front of her.. Which one is it?? Is it left or right???
In this scenario,
For the question, Where is the staffroom? Just answering it with a number ($10$ feet) is not enough.. We have to include the direction too..
Answering it like ‘$10$ feet left/right’ is the correct way.
🌾From this, we can say some questions cannot be answered just with a number. It has to be answered with a number and a direction.
Where is your house?
What is the velocity?
How much displacement?
🌾To define quantities like velocity, displacement, force, etc., we need a number (magnitude) and a direction, otherwise that definition will be incomplete.
Quantity that has to be defined with both its magnitude and direction is termed as a VECTOR.
Vector = magnitude + direction
- Temperature
- Distance
- Speed
- Length
- Area
- Volume
- Density
- Mass
- Electric current
- Displacement
- Velocity
- Differential length
- Differential area
- Force
- Momentum
- Weight