Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • please solve RD sharma class 12 chapter 22 Algebra of vector exercise 22 point 2 question 1 maths textbook solution

please solve RD sharma class 12 chapter 22 Algebra of vector exercise 22 point 2 question 1 maths textbook solution

Answers (1)

\vec{OA}+\vec{OB}+\vec{OC}=\vec{OD}+\vec{OE}+\vec{OF}…hence proved

Hint:

With the help of vector algebra.

Given:

D, E, F are the midpoints of BC, CA, and AB.

Solution :

Let us assume the position vectors of the midpoints D, E, F with respect to O are \vec{d},\vec{e}  and  \vec{f}respectively.

\vec{OD}=\vec{d},\vec{OE}=\vec{e} and \vec{OF}=\vec{f}

Now, D is the midpoint of side BC.

This means D divides BC in the ratio 1:1

 The position vector of point P which divides the AB, the line

 joining points A and B with position vectors \vec{a} and \vec{b}  respectively,

internally in the ratio m:n is,

\vec{p}=\frac{m\vec{b}+n\vec{a}}{m+n}

Here, m:n=1

\Rightarrow \vec{d}=\frac{(1)\vec{c}+(1)\vec{b}}{1+1}\\

\Rightarrow \vec{d}=\frac{\vec{b}+\vec{c}}{2}\\ \therefore \vec{b}+\vec{c}=2\vec{d}

Similarly, for midpoint E and Side CA , we get \vec{c}+\vec{a}=2\vec{e} and for midpoint F and side AB, we get \vec{a}+\vec{b}=2\vec{f}

Adding the three equations, we get

\begin{aligned} &\vec{b}+\vec{c}+\vec{c}+\vec{a}+\vec{a}+\vec{b}=2 \vec{d}+2 \vec{e}+2 \vec{f} \\ &\Rightarrow 2 \vec{a}+2 \vec{b}+2 \vec{c}=2 \vec{d}+2 \vec{e}+2 \vec{f} \\ &\Rightarrow 2 \overrightarrow{(a}+\vec{b}+\vec{c})=2(\vec{d}+\vec{e}+\vec{f}) \\ &\therefore \vec{a}+\vec{b}+\vec{c}=\vec{d}+\vec{e}+\vec{f} \end{aligned}

Thus,

\vec{OA}+\vec{OB}+\vec{OC}=\vec{OD}+\vec{OE}+\vec{OF}

Posted by

Info Expert 29

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question