And one property that we specifically look at is the change of vector components under rotation.
Let us see that.
(Refer Slide Time: 0:33)
Suppose you have a friend who asks you, how far is the house of another friend? And you say, it
is 500 m or you say, you walk 300 m to the east I am just taking the previous example, and 400
m to the north. So that the direct distance of that house is 500 m. But you have to walk in a
zigzag manner. In that you have to go east 1st and then north. Total distance you cover is 700 m.
Now suppose you have another friend who is looking at it from a different frame. So for the
previous friend, you had the X axis along the east and Y axis along the north. But another friend
has his axis X prime and this at some angle Theta from the east and Y prime at some angle Theta
from the north.
Although the distance travelled by this person in going to the other house is going to be 700 m in
both the frames, however this vector you can see is going to have components which are not
going to be 300 and 400 m. But this is going to be its X component and this is going to be its Y
component. So although the vector remains the same, it is 500 m in this north-east direction but
its components along different frames are different.
On the other hand, for the scalar quantity, distance, that remains the same, unchanged. So what
we conclude? A scalar quantity which is nothing but a number remains unchanged in the two