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  • Provide solution for RD Sharma maths class 12 chapter 27 Straight Line in Space exercise 27.1 question 18 maths textbook solution

Provide solution for RD Sharma maths class 12 chapter 27 Straight Line in Space exercise 27.1 question 18 maths textbook solution

Answers (1)

Answer :-

(\hat{\imath}+2 \hat{\jmath}-\hat{k})+\lambda(7 \hat{\imath}-5 \hat{\jmath}+\hat{k})

Hint :-

\overrightarrow{r}=\overrightarrow{a}+\lambda \overrightarrow{b}

Given :-

A(1,2,-1) \& 5 x-25=14-7 y=35 z

Solution :-

5 x-25=14-7 y=35 z \\ \Rightarrow \frac{x-5}{\frac{1}{5}}=\frac{y-2}{\frac{-1}{7}}=\frac{z}{\frac{1}{35}} \\ \Rightarrow \frac{x-5}{7}=\frac{y-2}{-5}=\frac{z}{1}  --------------  (1)

Direction ratios of (1)  will be ( 7 , -5 , 1 )

hence, \vec{b}=7 \hat{\imath}-5 \hat{\jmath}+\hat{k}

P.V of  A(1,2,-1)=>\vec{a}=\hat{\imath}+2 \hat{\jmath}-\hat{k} \\

\vec{r}=\vec{a}+\lambda \vec{b} \\ \quad

    =(\hat{\imath}+2 \hat{\jmath}-\hat{k})+\lambda(7 \hat{\imath}-5 \hat{\jmath}+\hat{k})

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