A Guide to Understanding Definition of Vector Quantities

In Physics, force, velocity, speed, and work are usually classified as scalar or vector quantities. Scalar quantities only have magnitude but no direction. Vectors consist of both magnitude and direction. A quantity that depends on the magnitude and direction like force, displacement, momentum, velocity, and acceleration is known as the vector quantity. It is denoted by a number and an arrow at the top (a) or a unit cap like a.

Example: Measuring the displacement or shortest distance covered by a car is vector quantity. 

Vector quantity

• The physical quantity that shows both magnitude and direction is a vector quantity.
• The vector quantity in one dimension can be represented by the positive (+) or negative sign (-).
• It expresses the physical quantity in both values (magnitude) and direction.
• Vectors are represented graphically as an arrow. It connects two points.
• Otherwise, it is represented by a line segment.
• Examples of vector quantity are: 

1. displacement 
2. velocity
3. acceleration
4. momentum
5. force
6. lift
7. drag
8. weight
9. angular velocity
10. magnetic polarisation
11. change in temperature
12. position

• One of the famous examples is force is a vector quantity because you can measure the quantity of force applied and the direction in which the force is applied.

Different types of vectors

Both scalars and vectors can represent the type of quality of any physical or mathematical object. There are eleven types of vectors. They are:

Zero vector or null vector

When the point of departure and the point of arrival of a vector coincide, it is known as a zero vector or null vector. It doesn’t have any magnitude and direction.

Position vector

It determines the position of an object or the location of any point concerning its origin. The starting point of the position vector is at the origin and may end at any point.

Co-initial vector or Concurrent vector

Co-initial means when the point of origin is the same. Two or more vectors starting at the same point are called co-initial vectors. They may move in any direction, but these vectors have the same starting points.

Like vectors

Here the vectors move in the same direction.

For example

• If car A and car B travel in the east direction, which is in the same direction, they are like vectors.

Unlike vector

Here both vectors travel in opposite directions

For example

• Let us consider the above example of two cars. If both cars, A and B, move in the opposite directions, they are called unlike vectors.

Coplanar vectors

Here all the vectors lie in the same plane. To become coplanar, certain conditions should be followed.

For example

• Consider three or more vectors in the 3D plane, and their scalar product is zero; then, these vectors are called coplanar vectors.
• If three vectors in the 3D plane are linearly independent, these vectors are called coplanar vectors.

Collinear vectors or parallel vectors

Irrespective of magnitude and direction, the vectors should be parallel to the same line regardless of magnitude and direction. The collinear vector should travel in the same line or parallel to each other in the same or opposite direction.

Equal vector

When two or more vectors travel in the same direction and have equal magnitude, they are equal vectors.

Displacement vector

When vectors move from one place to another, they are called displacement vectors.

Negative vector

Vectors that travel with the same magnitude but in opposite directions are called negative vectors.

Vector quantity example

• 10 metres in the north direction
• 45 m/sec in the west direction

These two are examples of vectors as directions are mentioned

The baseball player walked 20 miles an hour towards the end zone

Ans: It is a vector quantity as 20 miles represent the magnitude and the directions towards the end.

The bike accelerated west at the rate of 10 metres per second square.

Ans: It is a vector quantity as acceleration comes under it.

Scalars and vectors’ differences

Conclusion 

Vectors and scalars are concepts in mathematics that may be difficult to understand at first. On the other hand, with consistent study and comprehension. Here, we saw that there are ten types of vectors — the physical quantity, the magnitude, and direction. They are mathematical concepts, and there are different types of vectors, as discussed above. Vectors represent displacement, velocity, and acceleration and help define the force applied to a body simultaneously in the three dimensions.