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  • Explain Solution R.D.Sharma Class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 22 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 22 Maths Textbook Solution.

Answers (1)

Answer  : the angle cannot be made between AB and CD because both are parallel to each other

Given: the coordinates of the points A,B,C,D be (1,2,3);(4,5,7);(-4,3,-3);(2,9,2) respectively. Find angles between the lines AB and CD

Hint: \vec{CD}=2\vec{AB}

Solution:

\begin{aligned} &\vec{A}=(\hat{i}+2 \hat{j}+3 \hat{k}) \\ &\vec{B}=(4 \hat{i}+5 \hat{j}+7 \hat{k}) \\ &\vec{C}=(-4 \hat{i}+3 \hat{j}-6 \hat{k}) \\ \end{aligned}

\begin{aligned} &\vec{D}=(2 \hat{i}+9 \hat{j}+2 \hat{k}) \\ &\overrightarrow{A B}=3 \hat{i}+3 \hat{j}+4 \hat{k} \\ &\overrightarrow{C D}=6 \hat{i}+6 \hat{j}+8 \hat{k} \\ &\therefore C D=2 \overrightarrow{A B} \\ &=2(3 \hat{i}+3 \hat{j}+4 \hat{k}) \\ &=6 \hat{i}+6 \hat{j}+8 \hat{k} \end{aligned}

CD and AB are parallel. So it cannot make any angle

 

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