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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 2 sub question 2 maths textbook solution

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 2 sub question 2 maths textbook solution

Answers (1)

Answer: A,B and C are collinear

Hint: Try to form vectors such that one vector represents the another vector as a scalar product

\Rightarrow Given the points,

\begin{aligned} &A=2 \hat{i}-\hat{j}+3 \hat{k} \\ &B=4 \hat{i}+3 \hat{j}+\hat{k} \\ &C=3 \hat{i}+\hat{j}+2 \hat{k} \end{aligned}                                                        

\overrightarrow{AB} = Position of vector B – Position of vector A

\begin{aligned} &=(4 \hat{i}+3 \hat{j}+\hat{k})-(2 \hat{i}-\hat{j}+3 \hat{k}) \\ &=(4-2) \hat{i}+(3+1) \hat{j}+(1-3) \hat{k} \\ &=2 \hat{i}+4 \hat{j}-2 \hat{k} \\ &=2(\hat{i}+2 \hat{j}-\hat{k}) \end{aligned}                                      ............(1)         

 Similarly, \overrightarrow{BC} = Position of vector C – Position of vector B

 \begin{aligned} &=(3 \hat{i}+\hat{j}+2 \hat{k})-(4 \hat{i}+3 \hat{j}+\hat{k}) \\ &=(3-4) \hat{i}+(1-3) \hat{j}+(2-1) \hat{k} \\ &=-\hat{i}-2 \hat{j}+\hat{k} \\ &=-(\hat{i}+2 \hat{j}-\hat{k}) \end{aligned}                                     ............(2)

From (1) & (2)

\overrightarrow{AB}=-2\overrightarrow{BC}

Thus, both vectors are parallel to each other and as B being the common point

Given, Points A, B and C are collinear

 

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