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# Give a Condition that Three Vectors → a , → B and → C Form the Three Sides of a Triangle. What Are the Other Possibilities? - CBSE (Commerce) Class 12 - Mathematics

ConceptScalar Triple Product of Vectors

#### Question

Give a condition that three vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$  form the three sides of a triangle. What are the other possibilities?

#### Solution

Let $\text { ABC }$ be a triangle such that $\overrightarrow {BC} = \vec{a}$ $\overrightarrow{AB} = \vec{c}$ and $\overrightarrow{CA} = \vec{b}$. Then,    $\vec{a} + \vec{b} + \vec{c} = \overrightarrow{BC} + \overrightarrow{CA} +\overrightarrow{AB}$

$\vec{a} + \vec{b} + \vec{c} = \overrightarrow{BA} + \overrightarrow{AB}$

[∵ $\overrightarrow{BC} + \overrightarrow{CA} = \overrightarrow{BA}$]
$\Rightarrow \vec{a} + \vec{b} + \vec{c} = \overrightarrow{BB}$                               [ Using triangle law]
$\Rightarrow \vec{a} + \vec{b} + \vec{c}\to = \vec{0}$                                  [ By definition of null vector]
Other possibilities are
$\left( i \right) \vec{c} + \vec{a} = \vec{b}$
$\left( ii \right) \vec{a} + \vec{b} = \vec{c}$
$\left( iii \right) \vec{b} + \vec{c} = \vec{a}$

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Solution Give a Condition that Three Vectors → a , → B and → C Form the Three Sides of a Triangle. What Are the Other Possibilities? Concept: Scalar Triple Product of Vectors.
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