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Vectors and Its Types

ABCDE is a pe...

Question

$A B C D E$ is a pentagon. the resultant of the forces $\to A B + \to B C + \to D C + \to E D + \to A E = k \to A C$ , then find the value of $k$

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Solution

Given:- $A B C D E$ is apentagon and $\to A B + \to B C + \to D C + \to E D + \to A E = k \to A C$
To find:- $k = ?$
Sol:-
Let $R$ be the resultant force.
Therefore,
$R = \to A B + \to B C + \to A E + \to D C + \to E D + \to A C$
$R = (\to A B + \to B C) + (\to A E + \to E D + \to D C) + \to A C$
$R = \to A C + \to A C + \to A C$
$\Rightarrow R = 3 \to A C$
Now,
$∵ R = \to A B + \to B C + \to D C + \to E D + \to A E + \to A C$
$\Rightarrow R - \to A C = \to A B + \to B C + \to D C + \to E D + \to A E$
$\Rightarrow 3 \to A C - \to A C = k \to A C$
$\Rightarrow k = 2$

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