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  • please solve RD sharma class 12 chapter 22 Algebra of vector exercise 22.4 question 3 maths textbook solution

please solve RD sharma class 12 chapter 22 Algebra of vector exercise 22.4 question 3 maths textbook solution

Answers (1)

\vec{OA}+\vec{OB}+\vec{OC}+\vec{OD}=4\vec{OP}.....hence proved

Hint:

With the help of vector algebra.

Given:

A,B,C and D are the vertices of the quadrilateral.

Solution :

Using the triangle law in ?AOP

\vec{OP}+\vec{PA}=\vec{OA}           ?(i)

Using the triangle law in ?ABP

\vec{OP}+\vec{PB}=\vec{OB}            ?(ii)

Using the triangle law in ?OPC

\vec{OP}+\vec{PC}=\vec{OC}            ?(iii)

Using the triangle law in ?OPD

\vec{OP}+\vec{PD}=\vec{OD}            ?(iv)

Adding all the equations,

\begin{aligned} &\overrightarrow{O P}+\overrightarrow{P A}+\overrightarrow{O P}+\overrightarrow{P B}+\overrightarrow{O P}+\overrightarrow{P C}+\overrightarrow{O P}+\overrightarrow{P D}=\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O D}+\overrightarrow{O C} \\ &\overrightarrow{P A}+\overrightarrow{P B}+\overrightarrow{P C}+\overrightarrow{P D}+4 \overrightarrow{O P}=\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O D}+\overrightarrow{O C} \\ &4 \overrightarrow{O P}=\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O D}+\overrightarrow{O C} \ldots a s \overrightarrow{P A}=-\overrightarrow{P C} \& \overrightarrow{P B}=-\overrightarrow{P D} \end{aligned}

 

…hence proved

 

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