what is the difference between a vector & a scalar?

Answer 1

A general high school definition you get is that a vector has a direction and a scalar does not.

A more accurate definition is that some things in this world are best represented by one value and some are best represented by three values. Direction and position in our 3-dimensional world are best described in 3 dimenions, like a vector. Temperature is best described by one value, its a scalar. Its also interesting to note that some things in this world are even better represented as 9 values; these are called Tensors.

Answer 2

In physics, a scalar is a simple physical quantity that does not depend on direction, and therefore does not depend on the choice of a coordinate system.A physical quantity is expressed as the product of a numerical value and a physical unit, not just a number. It does not depend on the unit distancealthough the number depends on the unit. Thus distance does not depend on the length of the base vectors of the coordinate system. Also, other changes of the coordinate system may affect the formula for computing the scalar, but not the scalar itself. In this sense, physical distance deviates from the definition of metric in not being just a real number; however it satisfies all other properties. The same applies for other physical quantities which are not dimensionless.

In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. A vector has properties that do not depend on the coordinate system used to describe it. However, a vector is often described by a fixed number of components, each of which is dependent upon the particular coordinate system being used, such as Cartesian coordinates, spherical coordinates or polar coordinates.

A common example of a vector is force — it has a magnitude and an orientation and multiple forces sum according to the parallelogram law.

Answer 3

A vector has direction. A scalar does not.

eg. Velocity (vector) - gives distance/time in a particular direction.
c/w Speed (scalar) - gives distance/time


Town B is 100km north of town A
Motorist drives from A to B and then back to A and takes 4 hours.

Velocity is 0
Speed is 200/4 = 50kph

Assuming 2hr journey from A-B for the first half of the journey, motorist has average velocity 50kph North

Then coming back, B-A motorist has average velocity 50kph South.

Vector addition cancels this out.

Answer 4

A vector has the direction attribute. A scalar is only a absolute value. Ex. Seep is a scalar - 60 km/hr. Velocity is a vector 60km/hr North.

Answer 5

Suppose there is a water tank and if any one asks “How much water it can have?” we will answer him, ‘500 liters’.

We will not bother about the direction and we will not ask him “In which direction do you want the amount of water?”

These types of quantities which do not require a direction to understand it are called scalars.

Examples, energy, power, temperature, perimeter of an area, time etc.

Suppose there is a table in a room and if any one requests you to push the table, at once we will ask him, ‘to which direction do you want to push the table?’.

These types’ quantities which cannot be understood with out specifying a direction are called vectors.

Examples, Force, velocity, acceleration, momentum etc.

Vectors have both magnitude and direction; scalars have only magnitudes.

Answer 6

a vector has direction while a scalar does not!

Answer 7

vector has both magnitude and direction but scalar has only magnitude.

Answer 8

A vector has direction.

Answer 9

scalar doesnt come in -ve(-5kgs is not possible)
vector does come in -ve(-5m/sec is possible)