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  • Please Solve R.D.Sharma class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 2 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 27 Straight Line in Space Exercise 27.2  Question 2 Maths Textbook Solution.

Answers (1)

Answer : the lines are perpendicular to the given points showed

Given: show that the line through the points( 1 ,-1,2) and (3,4,-2) is perpendicular to the points (0,3,2) and (3,5,6)

hint: sum will solve by the help of the direction ratio

                \begin{aligned} &\mathrm{DR}=\left(x_{2}-x_{1}\right) \hat{i}+\left(y_{2}-y_{1}\right) \hat{j}+\left(z_{2}-z_{1}\right) \hat{k}\\ \end{aligned}

Solution: direction ratio of

             \begin{aligned} &Line_{1}=(3-1)_{,}(4+1),(-2-2)\\ \end{aligned}

                           \begin{aligned} &=2 \hat{i}+5 \hat{j}-4 \hat{k}\\ \end{aligned}

                               

Direction ratio of \begin{aligned} &Line_{2}=(3-0),(5-3),(6-2)\\ \end{aligned}

                                      \begin{aligned} &=3 \hat{i}+2 \hat{j}+4 \hat{k}\\ \end{aligned}

For showing perpendicular, \begin{aligned} &\text { } \mathrm{a}_{1} \mathrm{a}_{2}+\mathrm{b}_{1} \mathrm{~b}_{2}+\mathrm{c}_{1} \mathrm{c}_{2}=0\\ \end{aligned}

Now

                \begin{aligned} &3.2+10-16=6+10-16\\ \end{aligned}

                                      =0

Hence line1  and line2 are perpendicular to the points (showed)

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