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In Radius

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Question

If $\vec{a}$ , $\vec{b}$ , $\vec{c}$ represent the sides of a triangle taken in order, then write the value of $\vec{a} + \vec{b} + \vec{c} .$

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Solution

Let $A B C$ be a triangle such that $\vec{B C} = \vec{a}, \vec{C A} = \vec{b}$ and $\vec{A B} = \vec{c} .$ Then,
$\vec{a} + \vec{b} + \vec{c} = \vec{B C} + \vec{C A} + \vec{A B}$
$= \vec{B A} + \vec{A B} = \vec{0}$ [∵ $\vec{B C} + \vec{C A} = \vec{B A}$ ]

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