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Explain solution RD Sharma class 12 Chapter 27 Striaght Line in Space Exercise Very Short Answer question 18

Answers (1)

Answer:

Required answer is   \frac{-1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}

Hint:

Use the equation of a line in space.

Given:

\frac{4-x}{3}=\frac{y+3}{3}=\frac{z+2}{6}

Solution:

We have,

\frac{4-x}{3}=\frac{y+3}{3}=\frac{z+2}{6}

The equation of the given line can be rewritten as,

\frac{x-4}{-3}=\frac{y+3}{3}=\frac{z+2}{6}

The direction ratios of the line parallel to the given line are proportional to  -3,3,6

The direction cosines of the line parallel to the given line are proportional to

\begin{aligned} &\frac{-3}{\sqrt{(-3)^{2}+3^{2}+6^{2}}}, \frac{3}{\sqrt{(-3)^{2}+3^{2}+6^{2}}}, \frac{6}{\sqrt{(-3)^{2}+3^{2}+6^{2}}} \\ & \end{aligned}

=\frac{-1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}

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