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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA5 Marks
Question
Two like parallel forces $\overrightarrow{a}$ and$\overrightarrow{b}$ act on a rigid body at A and B respectively. If $\overrightarrow{P}$ and $\overrightarrow{Q}$ are interchanged in position, show that the point of application of the resultant will be displaced through a distance $\frac{P -Q}{P + Q}.AB$
✓

Answer

Let the forces $\overrightarrow{P}$ and $\overrightarrow{Q}$ act at A and B respectively. Let C be the point from where resultant passes
$\therefore \frac{\overrightarrow{P}}{CB} = \frac{\overrightarrow{Q}}{AC}= \frac{\overrightarrow{P} + \overrightarrow{Q}}{AB}$
$\Rightarrow AC = \frac{\overrightarrow{Q}.{AB}}{\overrightarrow{P} + \overrightarrow{Q}}$
When the forces are interchanged in position, let ' be the point from where resultant passes, then
$\Rightarrow AC = \frac{\overrightarrow{P}.{AB}}{\overrightarrow{P} + \overrightarrow{Q}}$
$\text{As P>Q, we get CC'} = AC'-AC \frac{\overrightarrow{P} - \overrightarrow{Q}}{\overrightarrow{P} + {\overrightarrow{Q}}} \times AB$

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