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#### Question

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 cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity? Are the two equal?

#### Solution

#### Similar questions

Can you associate vectors with (a) the length of a wire bent into a loop, (b) a plane area, (c) a sphere? Explain.

Pick out the only vector quantity in the following list:

Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.

Read each statement below carefully and state with reasons, if it is true or false:

The magnitude of a vector is always a scalar

Read each statement below carefully and state with reasons, if it is true or false:

Three vectors not lying in a plane can never add up to give a null vector.

Establish the following vector inequalities geometrically or otherwise:

(a) |**a ***+ ***b**| ≤ |**a**| + |**b**|

(b) |**a ***+ ***b**| ≥ ||**a**| − |**b**||

(c) |**a ***− ***b**| ≤ |**a**| + |**b**|

(d) |**a ***− ***b**| ≥ ||**a**| − |**b**||

When does the equality sign above apply?