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  • Provide solution for RD Sharma maths class 12 chapter Straight Line in Space exercise 27.3 question 6 sub question (i)

Provide solution for RD Sharma maths class 12 chapter Straight Line in Space exercise 27.3 question 6 sub question (i)

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Answer: The answer of the given question is that the line do not intersect each other.

 

Hint: Assume \lambda=\lambda_{1} \text { and } \mu=\mu_{1}

 

Given: \vec{r}=(\hat{\imath}-\widehat{\jmath})+\lambda(2 \hat{\imath}+\hat{k}) \text { and } \vec{r}=(2 \hat{\imath}-\hat{\jmath})+\mu(\hat{\imath}+\hat{\jmath}-\hat{k})

 

Solution: let’s first assume that the line intersect for \lambda=\lambda_{1} \text { and } \mu=\mu_{1}

Then, \left(2 \lambda_{1}+1\right) \hat{\imath}-\hat{\jmath}+\lambda_{1} \hat{k}=\left(2+\mu_{1}\right) \hat{\imath}+\left(\mu_{1}-1\right) \hat{\jmath}-\mu_{1} \hat{k}

Equations we get,

\begin{aligned} &\left(2 \lambda_{1}+1\right)=\left(2+\mu_{1}\right) &\ldots(i)\\\\ &-1=\mu_{1}-1 &\cdots(ii)\\\\ &\lambda_{1}=-\mu_{1} &\ldots(iii) \end{aligned}

Solving equation (ii) and (iii), we get  \lambda_{1}=\mu_{1}=0

Which doesn’t satisfy the equation (i) which is a contradiction.

Thus, the above lines are skew lines i.e. they neither intersect nor parallel to each other.

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