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Physics Part I

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Class 10 Class 12
Establish the vector inequalities geometrically or otherwise :
(d) |ab| > ||a| |b||

Let two vectors a and b be represented by the adjacent sides of a parallelogram PORS, as shown in the given figure.

The following relations can be written for the given parallelogram. 

OS + PS > OP                               ...(i) 

OS > OP - PS                                ...(ii) 

| a - b | > | a | - | b |                    ...(iii) 

The quantity on the LHS is always positive and that on the RHS can be positive or negative.

To make both quantities positive, we take modulus on both sides.

That is, 

| | a - b | | > | | a | - | b | | 

| a - b | > | | a | - | b | |                 ...(iv) 

If the two vectors act in a straight line but in the opposite directions, then we can write,

| a - b | = | | a | - | b | |                   ...(v)

Combining equations (iv) and (v), we get, 

| a - b | ≥ | | a | - | b | |  

Give three examples of scalar quantities.

Mass, temperature and energy

What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors. 


Give three examples of vector quantities.

Force, impulse and momentum.