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

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

Answer»

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