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Pure Rotation about an Axis

Forces with m...

Question

Forces with magnitudes proportional to $A B, B C$ and $2 C A$ act along the sides of a triangle $A B C$ in order. Their resultant is represented in magnitude and direction by:

A

C A

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B

A C

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C

B C

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D

C B

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Solution

The correct option is A $C A$
$\to A B + \to B C + \to C A = \to 0$ since $\to A B + \to B C = \to A C$ and $\to C A = - \to A C$
$∴ \to A B + \to B C + 2 \to C A = (\to A B + \to B C + \to C A) + \to C A = \to 0 + \to C A = \to C A$

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