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Class 10 Class 12

Establish the vector inequality:
(a) |b| ≤ |a| + |b|

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

Here, we can write:

OM = | a |                                 ...(i)

MN = OP = | b |                         ...(ii)

ON = | a + b |                            ...(iii)

In a triangle, each side is smaller than the sum of the other two sides.

Therefore, in ΔOMN, we have,

ON < (OM + MN)

| a + b | < | a | + | b |                 ...(iv)

If the two vectors a and b act along a straight line in the same direction, then we can write:

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

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

| a + b | ≤ | a | + | b |
112 Views

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views

Give three examples of scalar quantities.

Mass, temperature and energy
769 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

What is a scalar quantity?

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