Establish the vector inequalities geometrically or otherwise :
| a - b | ≥ || a | - | b ||Let two vectors a and b be represented by the adjacent sides of a parallelogram PORS, as shown in the given figure.
A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest taxi driver takes him along a circuitous path 23 km long and reaches the hotel in 28 minutes.
What is:
(a) the average speed of the taxi?
(b) the magnitude of average velocity? Are the two equal?
Given,
Magnitude of displacement = 10 km
Total path length = 23 km
Time taken = 28 min = 7/15 hr.
Therefore,
Magnitude of average velocity is,
Therefore, we can see that the average speed and magnitude of average velocity are not equal.
(a) The cyclist starts from O and again returns to point O. Therefore, the initial and the final point are the same. Hence, displacement of cyclist is equal to zero.
(b) Average velocity of cyclist is zero because total displacement of cyclist is zero.
(c) Total distance travelled by cyclist is,
∴ Average speed =
and
Time taken for round trip,
∴