How do you get a vector from the magnitude?  My teacher said that you should know how to change a magnitude to a vector, but I have no idea how to do it! Please give me an example with explanation!

krishna-agrawala | Student

I do not know in what context your teacher was talking about changing magnitude to a vector. So I will describe here some fundamental concepts associated with vectors.

All quantities are classified in two groups - scalars and vectors. Scalar quantities have only magnitude, for example, mass, length, time, volume, and speed.

Vector quantities have magnitude as well as direction. Some example of vector quantities are force, velocity and acceleration.

Perhaps the best way to understand the difference between scalar and vector quantities is to understand the difference between speed and velocity. When we are talking about the fastest ever train, it is enough to say that the speed of the train is 500 kilometer per hour. It is not necessary for us to know the direction of train's movement. However if we wanted to study the path taken by a cannon ball launched fired from a gun, it becomes important to know the angle and direction in which the cannon was fired.

When we want to add or subtract scalars quantity there is no concept of direction. If weight of a truck is 1 ton and it is carrying a consignment of 10 tons. the combined weight of the truck and the consignment is the addition of the two weights. This comes to 11 tons. But if we we were to calculate the rate of movement of an ant moving within the truck. We will need to know the direction of the ant's movement in relation to the direction of movement of the truck. If both are moving in the same direction, the net rate of movement or the magnitude of velocity will be addition of the two velocities of the truck and the ant. If they are moving in opposite direction the net velocity will be obtained by subtraction. If their movements are in some other directions then the net velocity cannot be obtained by simple addition or subtraction. We will need to use the method of vector addition.

A vector is often represented by a straight line. The length of the line represents the magnitude of the vector, and and the direction of line, marked by an arrow represents the direction of the vector.

neela | Student

A vector has two characteristics: (i) Magnitude and (ii) direction.

A force of  3 Newton  in eastern direction and another force  of 4newton in northern direction has resultant of magnitude in the direction of the diagonal of the rectangle of the sides 3 and 4 and is equal to 5.

We say a force of magnitude F in a particular direction has an effect of  F*cosx along a direction of angle x with the force F.