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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 19 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 27 Straight Line in Space  Exercise 27.2 Question 19 Maths Textbook Solution.

Answers (1)

Answer: The two lines are perpendicular to each other(shown)

Given: show that the lines \frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{1} and \frac{x}{1}=\frac{y}{2}=\frac{3}{2}are perpendicular to each other

Hint: for showing perpendicular \vec{b}.\vec{c}=0

Solution:

                Direction ratio_{1}=7\hat{i}-5\hat{j}+\hat{k}

                Direction ratio_{2}=\hat{i}-2\hat{j}+3\hat{k}

                \vec{b}.\vec{c}=0

                \begin{aligned} &\Rightarrow(7 \hat{i}-5 \hat{j}+\hat{k}) \cdot(\hat{i}+2 \hat{j}+3 \hat{k}) \\ &\Rightarrow 7-10+3=0 \end{aligned}

Therefore the two lines are perpendicular

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