Figure shows three vectors vector a, vector b and vec{c} , where R is midpoint of PQ . Then which of

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3-1.Vectors

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Figure shows three vectors $\vec{a}, \vec{b}$ and $\vec{c}$, where $R$ is the midpoint of $PQ$ . Then which of the following relations is correct?

A$\mathop {\,a}\limits^ \to \, + \mathop {\rm{b}}\limits^ \to \, = \,\,2\mathop {\,c}\limits^ \to $

B$\mathop {\,a}\limits^ \to \, + \mathop {\rm{b}}\limits^ \to \, = \,\,\mathop {\,c}\limits^ \to $

C$\mathop {\,a}\limits^ \to \, - \mathop {\rm{b}}\limits^ \to \, = \,\,2\mathop {\,c}\limits^ \to $

D$\mathop {\,a}\limits^ \to \, - \mathop {\rm{b}}\limits^ \to \, = \,\,\mathop {\,c}\limits^ \to $

Solution

Step 1: Applying triangle law of vector addition From triangle law of vector addition,
In $\triangle OPR$
$\vec{a}=\vec{c}+\overrightarrow{R P}$
and $\operatorname{In} \triangle ORQ$
$\overrightarrow{ b }=\overrightarrow{ c }+\overrightarrow{ RQ }$
Step $2:$ Equation solving
Adding $eq ^{ n }(1)$ and (2)
$\vec{a}+\vec{b}=2 \vec{c}+\overrightarrow{R P}+\overrightarrow{R Q}$
Since $R$ is midpoint of $PQ$, therefore $\overrightarrow{ RP }=-\overrightarrow{ RQ }$ $\Rightarrow \vec{a}+\vec{b}=2 \vec{c}+\overrightarrow{R P}-\overrightarrow{R P}$
$\Rightarrow \vec{a}+\vec{b}=2 \vec{c}$

Standard 11

Physics

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(IIT-2018)

If $\overrightarrow R$ is the resultant vector of two vectors $\overrightarrow A $ and $\overrightarrow B $, then $\overrightarrow {\left| R \right|} \,…\,\overrightarrow {\left| A \right|} \, + \,\overrightarrow {\left| B \right|} $.

easy

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$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$

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(AIPMT-2006)

Figure shows three vectors $\vec{a}, \vec{b}$ and $\vec{c}$, where $R$ is the midpoint of $PQ$ . Then which of the following relations is correct?

Solution

Similar Questions

Which of the following forces cannot be a resultant of $5\, N$ and $7\, N$ force………..$N$

The vector $\overrightarrow{O A}$ where $O$ is origin is given by $\overrightarrow{O A}=2 \hat{i}+2 \hat{j}$. Now it is rotated by $45^{\circ}$ anticlockwise about $O$. What will be the new vector?

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The vectors $\vec{A}$ and $\vec{B}$ are such that

$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$

The angle between the two vectors is