If OACB is a parallelogram with \[\overrightarrow{OC} = \vec{a}\text{ and }\overrightarrow{AB} = \vec{b} ,\] then \[\overrightarrow{OA} =\]

\[\frac{1}{2}\left( \vec{a} - \vec{b} \right)\]Given a parallelogram OACB such that \[\overrightarrow{OC} = \vec{a} , \overrightarrow{AB} = \vec{b}\]. Then,\[\overrightarrow{OB} + \overrightarrow{BC} = \vec{OC} \]\[ \Rightarrow \overrightarrow{OB} = \overrightarrow{OC} - \overrightarrow{BC}\]\[\Rightarrow \overrightarrow{OB} = \overrightarrow{OC} - \overrightarrow{OA}\] [∵ \[\overrightarrow{BC} = \overrightarrow{OA}\]]\[\Rightarrow \overrightarrow{OB} = \vec{a} - \overrightarrow{OA} . . . \left( 1 \right)\]Therefore,\[ \overrightarrow{OA} + \overrightarrow{AB} = \overrightarrow{OB} \]\[ \Rightarrow \overrightarrow{OA} + \vec{b} = \vec{a} - \overrightarrow{OA} \left[ \text { Using } \left( 1 \right) \right]\]\[ \Rightarrow 2 \overrightarrow{OA} = \vec{a} - \vec{b} \]\[ \Rightarrow \overrightarrow{OA} = \frac{1}{2} \left( \vec{a} - \vec{b} \right)\]

If Oacb is a Parallelogram with → O C = → a and → a B = → B , Then → O a = - Mathematics

प्रश्न

If OACB is a parallelogram with $\vec{O C} = \vec{a} and \vec{A B} = \vec{b},$ then $\vec{O A} =$

पर्याय

$(\vec{a} + \vec{b})$
$(\vec{a} - \vec{b})$
$\frac{1}{2} (\vec{b} - \vec{a})$
$\frac{1}{2} (\vec{a} - \vec{b})$

MCQ

उत्तर

$\frac{1}{2} (\vec{a} - \vec{b})$
Given a parallelogram OACB such that $\vec{O C} = \vec{a}, \vec{A B} = \vec{b}$ .
Then,
$\vec{O B} + \vec{B C} = \vec{O C}$
$\Rightarrow \vec{O B} = \vec{O C} - \vec{B C}$
$\Rightarrow \vec{O B} = \vec{O C} - \vec{O A}$ [∵ $\vec{B C} = \vec{O A}$ ]
$\Rightarrow \vec{O B} = \vec{a} - \vec{O A} . . . (1)$
Therefore,
$\vec{O A} + \vec{A B} = \vec{O B}$
$\Rightarrow \vec{O A} + \vec{b} = \vec{a} - \vec{O A} [Using (1)]$
$\Rightarrow 2 \vec{O A} = \vec{a} - \vec{b}$
$\Rightarrow \vec{O A} = \frac{1}{2} (\vec{a} - \vec{b})$

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Vectors and Their Types

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Q 17 Q 16 Q 18

पाठ 23: Algebra of Vectors - MCQ [पृष्ठ ७९]

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पाठ 23 Algebra of Vectors
MCQ | Q 17 | पृष्ठ ७९

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If Oacb is a Parallelogram with → O C = → a and → a B = → B , Then → O a = - Mathematics

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