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If $C$ is the mid point of $AB$ and $P$ is any point outside $AB$ , then

Option 1)
$\overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC}=0$

Option 2)
$\overrightarrow{PA}+\overrightarrow{PB}+2\overrightarrow{PC}=\overrightarrow{0}$

Option 3)
$\overrightarrow{PA}+\overrightarrow{PB}=\overrightarrow{PC}$

Option 4)
$\overrightarrow{PA}+\overrightarrow{PB}=2\overrightarrow{PC}$

Answers (1)

best_answer

As we have learned

Position Vector -

If $\vec{a}$ and $\vec{b}$ are the position of vectors of two points A and B then

$\overrightarrow{AB}= \vec{b}-\vec{a}$

$\overrightarrow{AB}= P \vee of B - P\vee of A$

- wherein

Mid point formula -

$\frac{\vec{a}+\vec{b}}{2}$

- wherein

If $\vec{a}$ and $\vec{b}$ , position vector of mid-point of AB

$\vec{PA}+\vec{PB} = (-\vec{P}+\vec{a })+ (\vec{-P}+\vec{b})\\= -2 \vec{P}+ (\vec{a}+\vec{b })$

$\vec{PC} = \frac{\vec{a}+\vec{b }-2\vec{P}}{2}\\$

$= \frac{\vec{PA}+\vec{PB}}{2}$

$= {\vec{PA}+\vec{PB}}= 2 \vec{PC}$

Option 1)

$\overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC}=0$

Option 2)

$\overrightarrow{PA}+\overrightarrow{PB}+2\overrightarrow{PC}=\overrightarrow{0}$

Option 3)

$\overrightarrow{PA}+\overrightarrow{PB}=\overrightarrow{PC}$

Option 4)

$\overrightarrow{PA}+\overrightarrow{PB}=2\overrightarrow{PC}$

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Himanshu

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