Question

S=(2i+3j-5k)m and (6I-5j-4k)N what is work done by this force

Answer 1

Given :

• $\sf{\vec S \: = \: (2 \hat{i} \: + \: 3 \hat{j} \: - \: 5 \hat{k}) \: m}$
• $\sf{\vec F \: = \: (6 \hat{i} \: - \: 5 \hat{j} \: - \: 4 \hat{k}) \: N}$

To Find :

• Work Done by Force

Solution :

As we know that,

$\implies \sf{W \: = \: \vec F. \vec S}$

Where,

• W is Work Done
• F is force
• S is Displacement

Putting Values of $\sf{\vec F \: \: and \: \: \vec{S}}$,

$\implies \sf{W \: = \: \big[ (2 \hat{i} \: + \: 3 \hat{j} \: - \: 5 \hat{k}) . (6 \hat{i} \: - \: 5 \hat{j} \: - \: 4 \hat{k}) \big]} \\ \\ \implies \sf{W \: = \: \big[ (2 \: \times \: 6) \: + \: (3 \: \times \: -5) \: + \: (-5 \: \times \: -4) \big]} \\ \\ \implies \sf{W \: = \: (12 \: - \: 15 \: + \: 20)} \\ \\ \implies \sf{W \: = \: 32 \: - \: 15} \\ \\ \implies \sf{W \: = \: 17}$

$\therefore$ Work Done is 17 J

$\rule{150}{2}$

Some Important Points :

• There are two types of Quantities vector and scalar.

• Vectors are those quantities which have magnitude as well are direction.

• Scalar quantities are those which have only magnitude, no direction.

• Example of vector quantities are acceleration, force, displacement, etc.

• Example of scalar quantities are Work Done, Speed, distance, etc.

• Product of Two vector quantities is always a scalar quantity