﻿ Establish the vector inequalities geometrically or otherwise :(c) |a−b| < |a| + |b| from Physics Motion in A Plane Class 11 Manipur Board

## Book Store

Currently only available for.
CBSE Gujarat Board Haryana Board

## Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12
Establish the vector inequalities geometrically or otherwise :
(c) |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.

Here we have:

| OR | = | PS | = | b |              ...(i)

| OP | = | a |                          ...(ii)

In a triangle, each side is smaller than the sum of the other two sides. Therefore, in ΔOPS, we have:

OS < OP + PS

| a - b | < | a | + | -b |

| a - b | < | a | + | b |            ... (iii)

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

| a - b | = | a | + | b |             ... (iv)

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

| a - b | ≤ | a | + | b |
101 Views

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views

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.

814 Views

What is a vector quantity?

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

Give three examples of scalar quantities.

Mass, temperature and energy
769 Views

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views