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  • Please Solve R.D.Sharma class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 5 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 5 Maths Textbook Solution.

Answers (1)

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

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

Hint: For showing perpendicular a.b must be equal to ‘ 0’

Solution: \frac{x-5}{7}=\frac{y+2}{-5}=\frac{Z}{1}

                Direction: ratio = 7,-5,1

                Vector \vec{a}=7\hat{i}-5\hat{j}+\hat{k}

Again,

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}

\begin{aligned} &\therefore \text { Direction ratios }=1,2,3 \\ \end{aligned}

\begin{aligned} &\therefore \vec{b}=\hat{i}+2 \hat{j}+3 \hat{k} \\ \end{aligned}

               \begin{aligned} &\vec{a} \cdot \vec{b}=7-10+3 \\ &=0 \end{aligned}               

So the given two lines are perpendicular to each other (showed)

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