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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 1 sub question 1 maths textbook solution

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 1 sub question 1 maths textbook solution

Answers (1)

Answer: Vectors are collinear

Hint: Prove one vector representing in the form of another vector

\Rightarrow Given   Let

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

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

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

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

\begin{aligned} &=(\hat{i}+4 \hat{j}-3 \hat{k})-(3 \hat{i}-2 \hat{j}+\hat{k}) \\ &=(1-3) \hat{i}+(4+2) \hat{j}+(-3-1) \hat{k} \\ &=-2 \hat{i}+6 \hat{j}-4 \hat{k} \\ &=-2(\hat{i}-3 \hat{j}+2 \hat{k}) \end{aligned}

 From (1) we can say

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

Also, B is the common point and \overrightarrow{BC} and\overrightarrow{AB} are parallel

Hence, Vectors are collinear

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