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  • Provide solution for RD Sharma maths class 12 chapter 27 Straight Line in Space exercise 27.1 question 15 maths textbook solution

Provide solution for RD Sharma maths class 12 chapter 27 Straight Line in Space exercise 27.1 question 15 maths textbook solution

Answers (1)

Answer :-  The points are collinear

Hint :-

\frac{x-x_{1}}{x_{2}-x_{1}}=\frac{y-y_{1}}{y_{2}-y_{1}}=\frac{z-z_{1}}{z_{2}-z_{1}}

 Given :-

P.V are 2 \hat{\imath}+3 \hat{\jmath}, \hat{\imath}+2 \widehat{\jmath}+3 \hat{k}, 7 \hat{\imath}+9 \hat{k}  

Solution :-

The points of P.V 2 \hat{\imath}+3 \hat{\jmath}, \hat{\imath}+2 \widehat{\jmath}+3 \hat{k}, 7 \hat{\imath}+9 \hat{k}  are (-2 , 3 , 0) , (1 , 2 , 3) , (7 , 0 , 9)

The equation of the line passing through the point (-2,3,0) and (1 , 2 , 3) are

\begin{aligned} &\frac{x+2}{1+2}=\frac{y-3}{2-3}=\frac{z-0}{3-0} \\ &\Rightarrow \frac{x+2}{3}=\frac{y-3}{-1}=\frac{z-0}{3} \end{aligned} ----- (1)

Putting (7 , 0 , 9) in (1) , we get

\begin{aligned} &\frac{7+2}{3}=\frac{0-3}{-1}=\frac{9}{3} \\ \end{aligned}

\Rightarrow 3,3,3

Since ( 7 , 0 , 9) satisfying equation (1)

Hence it is collinear.

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