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#### Question

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.

#### Solution

#### Similar questions

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?

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.

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

Three girls skating on a circular ice ground of radius 200 m start from a point Pon the edge of the ground and reach a point Qdiametrically opposite to P following different paths as shown in Figure. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of the path skated?

State, for each of the following physical quantities, if it is a scalar or a vector: volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.