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  • Need solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 11

Need solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 11

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Final Answer:  -\left(\frac{-6}{7}, \frac{-2}{7}, \frac{-3}{7}\right) \text { or }\left(\frac{6}{7}, \frac{2}{7}, \frac{3}{7}\right)

Hint:

Use direction ratio of the line

Given:

Points (4, 3,-5) and (-2, 1,-8)

To Find: 

Direction cosine of line joining point

Solution:

Let point P(4, 3,-5)  and  Q (-2, 1,-8)  are joined to form line PQ
Direction Ratio of line PQ= Position vector of P- Position vector of  Q
Direction ratio of line PQ=[4-(-2), 3-1, -5-(-8)]

(a,b,c)=(6, 2, 3)

Direction Cosine of line PQ are:

l=\frac{a}{\sqrt{a^{2}+b^{2}+c^{2}}}, m=\frac{b}{\sqrt{a^{2}+b^{2}+c^{2}}}, n=\frac{c}{\sqrt{a^{2}+b^{2}+c^{2}}}

l=\frac{6}{\sqrt{6^{2}+2^{2}+3^{2}}}, m=\frac{2}{\sqrt{6^{2}+2^{2}+3^{2}}}, n=\frac{3}{\sqrt{6^{2}+2^{2}+3^{2}}}

\begin{aligned} &l=\frac{6}{\sqrt{49}}, m=\frac{2}{\sqrt{49}}, n=\frac{3}{\sqrt{49}} \\\\ &l=\pm \frac{6}{7}, m=\pm \frac{2}{7}, n=\pm \frac{3}{7} \end{aligned}

\begin{aligned} &(l, m, n)=\left(\frac{-6}{7},-\frac{2}{7}, \frac{-3}{7}\right) \\\\ &\text { or }\left(\frac{6}{7}, \frac{2}{7}, \frac{3}{7}\right) \end{aligned}

Therefore the direction cosine of the line segment are  \left(\frac{-6}{7}, \frac{-2}{7}, \frac{-3}{7}\right) \text { or }\left(\frac{6}{7}, \frac{2}{7}, \frac{3}{7}\right)

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