here you find the actual meaning of scalar and vector quantity. If we define scalar and vector quantity in simple word we can say that scalar quantity are those which have only magnitude not direction, but vector quantity are those which have both magnitude as well as direction. difference between scalar and vector quantity are given below the page for better understanding of these quantities.
There are many topics covered in this articles like,
- What is scalar and vector quantity?
- List of scalar and vector quantities and their units.
- Difference between scalar and vector quantity.
- Product of scalar and vector quantity.
- What is scalar and vector field?
- 20 examples of scalar and vector quantity.
- characteristics of scalar and vector quantities.
- Types of vector.
- vector addition and subtraction.
- What is scalar and vector quantity?
What is scalar and vector quantity?
scalar quantity:- Those quantity which has only magnitude not direction are called scalar quantity.
for example length, mass, speed, work, density, volume etc.
lets understand by taking examples If we say the body have 10 kg of mass it doesn’t means not 10 kg of mass in north or south direction.
In other words Those quantity which has only one dimension described by single element like one constant and one variable. for example 5m, 6cm, 2kg, 4mm etc.
Vector quantity:- Those quantity which has both magnitude and a specific direction are called vector quantity.
for example Displacement, Force, acceleration, velocity, torque, momentum etc.
lets understand by taking examples, suppose 2N of force act on the body in North direction, A body is accelerating 5m/s2 in upward direction, Weight (W= mg) of a body acted in the downward direction.
In other word Those quantity which has both two dimension and three dimension described by some more elements like 5m North, 3m/s2, 6m/s, 5N, etc.
List of scalar and vector quantities and their units.
| scalar quantity | unit of scalar quantity | vector quantity | unit of vector quantity |
| Mass | kilogram(kg) | Displacement | meter(m) |
| Distance | Meter(m) | Velocity | m/s |
| Time | Second(s) | Acceleration | m/s2 |
| Speed | m/s | Force | Newton(N) |
| Volume | m3 | Torque | Newton meter(N-m) |
| Density | kg/m3 | Electric field | volt per meter(v/m) |
| Pressure | Newton(N) | Angular velocity | radians per second |
| Work | Joule(J) | Linear momentum | kilogram meters per second(kg m/s) |
| Energy | Joule(J) | Magnetic dipole moment | Ampere meter(A-m) |
| Electric current | Ampere(A) | Thrust | Force(F) |
20 examples of scalar and vector quantity.
20 examples of scalar quantities
- Mass
- Distance
- Time
- Speed
- Volume
- Density
- Pressure
- Work
- Energy
- Electric Current
- Length
- Refractive Index
- Area
- Power
- Heat
- Temperature
- Size
- Calories
- Frequency
- Cost
20 examples of vector quantities
- Displacement
- Velocity
- Torque
- Thrust
- Force
- Acceleration
- Electric field
- Angular momentum
- Angular velocity
- Drift velocity
- Magnetic dipole moment
- Linear momentum
- Average velocity
- Magnetic field
- Weight
- Gravitational force
- vector potential
- Poynting vector
- current density
- Magnetisation
Difference between scalar and vector quantity.
These are some differential points on scalars and vectors.
Scalar quantity:-
- Scalar quantity has only magnitude.
- They change if their magnitude change.
- They can be added according to ordinary laws of algebra.
Vector quantity:-
- vectors have both magnitude and direction
- They change if either their magnitude, direction or both change.
- They can be added only by using special laws of vector addition.
Product of scalar and vector quantity
Scalar product and vector product are the two different ways of multiplying two vectors. Multiplication of scalar product has its own rule and Multiplication of vectors product has its own way.
Scalar product (or dot product) of two vectors:- The scalar or dot product of two vectors A and B is defined as the product of the magnitudes of vectors A and B and cosine of the angle θ between them.vector product (or cross product) of two vectors:- The vector or cross product of two vectors is defined as the vector whose magnitude is equal to the product of the magnitudes of two vectors and sine of the angle between them and whose direction is perpendicular to the plane of the two vectors.
What is scalar and vector field?
A scalar field is something that has a particular value at every point in space. for example temperature at every point on the earth has a particular value but if we move to and fro from that point then the value of temperature will change.A vector field is just similar to scalar field because vector field also having a value at every point on space. but it has a value and direction at every point in space.
characteristics of scalar and vector quantities.
Before knowing the characteristic of scalar and vector quantities. we have to know he meaning of characteristic.
characteristic means a quality of something that makes him/her/it different from other people or thing.
so here characteristic of scalar and vector quantity has little same that is magnitude. lets understand it in more detailed.
characteristic of scalar quantities:- scalar quantity has only magnitude. there is no need of direction. speed, distance, time, temperature these all do not need direction.
for example Ramesh played for 3 hours. here we do not need direction.
characteristic of vector quantities:- vector quantities has also magnitude but it needs direction for their illustration. displacement, velocity, acceleration, force etc acquires direction.
for example a body start moving by 3m/s in forward direction. here direction included for better illustration.
Types of vector.
Position vector:- A vector which gives position of an object with reference to the origin of a co-ordinate system is called position vector.
Displacement vector:- It is that vector which tells how much and in which direction and object has changed its position in a given time interval.
Polar vector:- The vector which has a starting point or a point of application are called polar vector.
Axial vector:- The vector which represent rotational effect and act along the axis of rotation in right hand screw rule are called axial vector.
Equal vector:- Two vectors are said to be equal if they have the same magnitude and same direction.
Negative of a vector:- The negative of a vector is defined as another vector having the same magnitude but having an opposite direction.
Modulus of vector:- The modulus of a vector means the length or the magnitude of that vector.
Unit vector:– A unit vector is a vector of unit magnitude drawn in the direction of a given vector.
Fixed vector:- The vector whose initial point is fixed is called a fixed vector.
Zero vector:- a zero vector or null vector is a vector that has zero magnitude and an unknown direction.
vector addition and subtraction.
Two vectors can be added or can be subtracted by their rules and laws. vectors can be added by two famous laws
- Triangle law of vector addition:- If two vectors can be represented both in magnitude and direction by the two sides of triangle taken in the same order, then their resultant is represented completely, both in magnitude and direction, by the third side of the triangle taken in the opposite order.
- Parallelogram law of vector addition:- If two vectors can be represented both in magnitude and direction by the two adjacent sides of a parallelogram drawn from a common point, then their resultant is completely represented, both in magnitude and direction, by the diagonal of the parallelogram passing through the point. see the above picture for more illustration.
Please note that the same rules and theory also use in subtraction of two vectors but you have to replace plus sign from the minus sign.
FAQ on scalar and vector quantities
What is scalar and vector quantities?
scalar quantities are those quantities which has only magnitude not direction. speed, time, distance etc.
vector quantities are those quantities which has both magnitude and a specific direction. displacement, velocity, acceleration etc.
Is work scalar or vector?
work is scalar quantity which has only magnitude. w= f.s work is dot product of force and displacement. and we know that dot product is scalar quantity.
can a scalar be negative?
Yes scalar can be negative. but it depends on situation and types of quantities. like temperature can be negative which is a scalar quantity.
Is force a scalar quantity?
No force is a vector quantity. because it has cross product of mass and acceleration. F= m✖️a cosθ.
Where do we use vectors?
vectors can be used in physics to represent physical quantities with direction in the upper head by arrow sign. it is used to represent displacement, velocity, acceleration, etc.
Where do we use vectors?
vectors can be used in physics to represent physical quantities with direction in the upper head by arrow sign. it is used to represent displacement, velocity, acceleration, etc.
Can you square a vector?
No we cannot square a vector because a vector has both magnitude and direction. we can square its magnitude but not direction.