Question

(i) Calculate the work done when $F=(5\hat{i}+3\hat{j}+2\hat{k})NandS=(3\hat{i}-\hat{j}+2\hat{k})$m acting in the same direction.
(ii) Show with the help of a vector diagram that the work done is scalar product of force and displacement.

Answer 1

Given that,

Force $\overrightarrow{F}=5\hat{i}+3\hat{j}+2\hat{k}$

Displacement $\overrightarrow{s}=3\hat{i}-\hat{j}+2\hat{k}$

We know that,

The work done is

$W=\overrightarrow{F}\cdot \overrightarrow{s}$

$W=(5\hat{i}+3\hat{j}+2\hat{k})\cdot (3\hat{i}-\hat{j}+2\hat{k})$

$W=15-3+4$

$W=16J$

Hence, this is the required solution

(b). we know that,

Work done = force ∙ displacement

$W=\overrightarrow{F}\cdot \overrightarrow{d}$

$W=Fd\cos \theta$

Where, $\theta$ is the angle between $\overrightarrow{F}$ and $\overrightarrow{d}$

This is a scalar product and work is a scalar