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  • Please Solve R.D.Sharma class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 8 Sub Question 1 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 8 Sub Question 1 Maths Textbook Solution.

Answers (1)

Answer: the angles between the lines will be 0^{0}

Given : find the angle between the points of lines

            \vec{r}=(4 \hat{i} - \hat{j})+8(\hat{i}+2 \hat{j}-2 \hat{k}) and

            \vec{r}=(\hat{i}-\hat{j}+2 \hat{k})-\mu[2 \hat{i}+4 \hat{j}-4 \hat{k}] \\    

Hint: \cos \theta= \frac{\overline{b_{1}} \cdot \overline{b_{2}}}{\left|b_{1}\right| \cdot\left|b_{2}\right|}

Solution:

                The 1st line is parallel to b1= (i+2j-2k) and the 2nd  line is parallel to b2 = (2i+4j-4k)

If \theta be an angle between the lines , so \theta will be the angle between b1&b2

           So,\begin{aligned} &\cos \theta=\frac{2+8+8}{\sqrt{2^{2}+2^{2}(-2)} \sqrt{2^{2}+4^{2}+\left(-4^{2}\right)}} \\ \end{aligned}

                        \begin{aligned} &=\frac{18}{\sqrt{9 \mid \sqrt{36}}} \\ &=\frac{18}{3 \times 6} \\ &\quad=1 \\ &\cos \theta=\cos 0 \\ &\theta=0^{\circ} \end{aligned}

The angle between with the lines will be 0^{0}

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