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  • Explain Solution R.D.Sharma Class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 25 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 25 Maths Textbook Solution.

Answers (1)

Answer: the value of k will be ‘2’

Given: find the value of k so that the lines x-y=kz \: and \: \: x-2y=2y+1 = -z+1 are perpendicular to each other.

Hint: when two lines are perpendicular then dot product will be equal to ‘0’

Solution: from equ (i)

             x=y=kz=\frac{x}{1}=\frac{y}{-1}=\frac{3}{1/k}

From equation (ii)

                \frac{x-2}{1}=\frac{y+1/2}{1/2}=\frac{z-1}{-1}

Since two straight lines are perpendicular to each other then

\begin{aligned} &a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=0 \\\\ &(1)+(-1 / 2)+(-1 / k)=0 \\\\ &\frac{2-1}{2}=\frac{1}{k} \\\\ &1 / 2=1 / \mathrm{k} \\\\ &\mathrm{K} \quad=2 \end{aligned}

 

                So the answer will be ‘2’

 

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