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  • Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26.1 question 3 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26.1 question 3 maths textbook solution

Answers (1)

Answer:\frac{3}{\sqrt{77}},\frac{-2}{\sqrt{77}},\frac{8}{\sqrt{77}}

Hint: Direction ratios are proportional to the length of line

Given: Two points (-2, 4, -5) and (1, 2, 3)

Solution:

The direction ratios of the line joining the two points are

(a, b, c) = (1-(-2), 2-4, 3-(-5))

(a, b, c)=(3, -2, 8)

Now, if l, m and n are the direction cosine, So

              \begin{aligned} &(1, \mathrm{~m}, \mathrm{n})=\left(\frac{\mathrm{a}}{\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}}}, \frac{\mathrm{b}}{\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}}}, \frac{\mathrm{c}}{\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}}}\right) \\ &(1, \mathrm{~m}, \mathrm{n})=\left(\frac{3}{\sqrt{3^{2}+(-2)^{2}+8^{2}}}, \frac{-2}{\sqrt{3^{2}+(-2)^{2}+8^{2}}}, \frac{8}{\sqrt{3^{2}+(-2)^{2}+8^{2}}}\right) \\ &(1, \mathrm{~m}, \mathrm{n})=\left(\frac{3}{\sqrt{77}}, \frac{-2}{\sqrt{77}}, \frac{8}{\sqrt{77}}\right) \end{aligned}

Therefore, the direction cosines of the line are \frac{3}{\sqrt{77}},\frac{-2}{\sqrt{77}},\frac{8}{\sqrt{77}}

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