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  • Please Solve R.D.Sharma class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 3 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 27 Straight Line in Space Exercise 27.2  Question 3 Maths Textbook Solution.

Answers (1)

Answer: The given two lines will be parallel  through the two points equal to ‘0’ showed;

Given: Show that the line through the points(4,7,8) and (2,3,4) is parallel to the line through the points (-1,-2,1) and (1,2,5)

Hint: for showing parallel v1 and v2 must be equal to ‘0’

Solution: 

\begin{aligned} &\vec{v}_{1}=(4-2) \hat{i}+(7-3) \hat{j}+(8-4) \hat{k} \\ &\overrightarrow{v_{1}}=2 \hat{i}+4 \hat{j}+4 \hat{k} \\ &\overline{v_{2}}=(1+1) \hat{i}+(2+2) \hat{j}+(5-1) \hat{k} \\ &\overline{v_{2}}=2 \hat{i}+4 \hat{j}+4 \hat{k} \end{aligned}

Now, \begin{aligned} \cos \theta=\cos \theta &=\frac{\overrightarrow{v_{1}} \overline{v_{2}}}{\left|\overrightarrow{v_{1}}\right|\left|\overrightarrow{v_{2}}\right|} \\ \end{aligned}

                                       \begin{aligned} &=\frac{4+16+16}{\sqrt{36} \sqrt{36}} \\ \end{aligned}

                                   \begin{aligned} =& \frac{36}{36} \\ \end{aligned}

                                       \begin{aligned} &=1 \\ \end{aligned}

                      \begin{aligned} \cos \theta &=1 \\ \end{aligned}

                      \begin{aligned} \cos \theta=\cos 0^{\circ} \\ \end{aligned}

                                    \begin{aligned} \theta=0^{\circ} \\ \end{aligned}

                                     \begin{aligned} \mathrm{v}_{1} \| \mathrm{v}_{2} \text { (proved) } \end{aligned}

So the two lines are parallel to each other

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