Question

Forces proportional to $AB$,$BC$and $2CA$act along the sides of triangle $ABC$ in order, their resultants represented in magnitude and direction is

• A. $CA$
• B. $AC$
• C. $BC$
• D. $CB$

Answer 1

The correct option is A

$CA$

Step 1. Given Data,

Forces are proportional to$AB$ $BC$and $2CA$act along the sides of the triangle $ABC$.

We have to find their resultants represented in magnitude and direction.

Step 2. We have to find their resultants

Resultant $AB+BC+2CA=AC+2CA$(Since, the resultant of $AB+BC=AC$ by vector triangle law)

But in the figure, the direction of the resultant is from $C$ to $A$ hence, putting $AC$$=-CA$we have,

$$\begin{gathered} \Rightarrow AB+BC+2CA=-CA+2CA \\ \Rightarrow AB+BC+2CA=CA \end{gathered}$$

Hence, the correct option is$\text{'}A\text{'}$.