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  • Please Solve R.D.Sharma class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 6 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 6 Maths Textbook Solution.

Answers (1)

Answer: the line joining by the point (2,1,1)  is perpendicular to the line determined by the other two points

Given: show that the line joining to the point (2,1,1) is perpendicular to the line determined by the points (3,5,-1) and (4,3,-1)

Hint:

                Direction ratio\left (x _{2}-0 \right ),\left ( y_{2}-0 \right ),\left ( z_{2}-0 \right )because line passes through origin

Solution:

            \begin{aligned} &v_{1}=(2-0) \hat{i}+(1-0) \hat{j}+(1-0) \hat{k} \\ &v_{1}=2 \hat{i}+\hat{j}+\hat{k} \\ &v_{2}=(4-3) \hat{i}+(3-5) \hat{j}+(-1+1) \hat{k} \\ &v_{2}=\hat{i}-2 \hat{j} \end{aligned}

Now from \begin{aligned} v_{1} \cdot v_{2} &=0 \\ \end{aligned}

             \begin{aligned} v_{1} v_{2} &=2-2 \\ &=0 \end{aligned}

So the line joining to the point (2,1,1) is perpendicular to the line joining by the determined points (3,5,-1) and (4,3,-1)

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