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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 1 sub question 2 maths textbook solution

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 1 sub question 2 maths textbook solution

Answers (1)

Answer: Vectors are collinear

Hint: Find PQ and QR

\Rightarrow Given

\begin{aligned} &P=3 \hat{i}-2 \hat{j}+4 \hat{k} \\ &Q=\hat{i}+\hat{j}+\hat{k} \\ &R=-\hat{i}+4 \hat{j}-2 \hat{k} \end{aligned}

Solution:

Let P,Q  and R be the points represented and the factor vectors are

\begin{aligned} &P=3 \hat{i}-2 \hat{j}+4 \hat{k} \\ &Q=\hat{i}+\hat{j}+\hat{k} \\ &R=-\hat{i}+4 \hat{j}-2 \hat{k} \end{aligned}

\overrightarrow{PQ} = Position of vector Q – Position of vector P

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

\overrightarrow{QR} = Position of vector R – Position of vector Q

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

Here, \overrightarrow{PQ}=\overrightarrow{QR}   

So, they are parallel to each other and B bring the common point implies that vectors are all collinear.

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