Wednesday, July 11, 2012

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...

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.

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