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Eccentricity of Ellipse

If a →, b →, ...

Question

If $\vec{a}$ , $\vec{b}$ , $\vec{c}$ are position vectors of the vertices A, B and C respectively, of a triangle ABC, write the value of $\vec{A B} + \vec{B C} + \vec{C A} .$

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Solution

Given: $\vec{a}, \vec{b}$ and $\vec{c}$ are the position vectors of $A, B$ and $C$ respectively. Then,
$\vec{A B} = \vec{b} - \vec{a} \vec{B C} = \vec{c} - \vec{b} \vec{C A} = \vec{a} - \vec{c}$
Consider,
$\vec{A B} + \vec{B C} + \vec{C A} = \vec{b} - \vec{a} + \vec{c} - \vec{b} + \vec{a} - \vec{c} = \vec{0}$

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