The direction cosines of the line which is perpendicular to the lines with direction cosines proportional to $(1, - 2, - 2)$ & $(0, 2, 1)$ are

(\frac{2}{3}, - \frac{1}{3}, \frac{2}{3})

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(\frac{2}{3}, \frac{1}{3}, \frac{2}{3})

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(\frac{2}{3}, \frac{1}{3}, \frac{- 2}{3})

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(\frac{- 2}{3}, \frac{1}{3}, \frac{2}{3})

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Solution

The correct option is A $(\frac{2}{3}, - \frac{1}{3}, \frac{2}{3})$
$\begin{matrix} A c c o r d i n g t o t h e q u e s t i o n : d i r e c t i o n r a t i o e q u : a, b, c a n d t w o l i n e i s p e r p e n d i c u l a r : (1, - 2, - 2,) & (0, 2, 1) r e l a t i o n o f d i r e c t i o n r a t i o w i t h p e r p e n d i c u l a r l i n e i s : \Rightarrow a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0 a - 2 b - 2 c = 0 0 a + 2 b + c = 0 - ---------------- - t h e r a t i o o f 3 d i r e c t i o n p o i n t i s : \frac{a}{2} = \frac{- b}{0} = \frac{c}{2} s o t h e r a t i o i s (\frac{2}{3}, \frac{- 1}{3}, \frac{2}{3}) a n d t h e c o r r e c t o p t i o n i s A . \end{matrix}$

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Similar questions

Q. Can

\frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}}, \frac{- 2}{\sqrt{3}}

be the direction cosines of any directed line?

Q. Find the direction cosines of the line which is perpendicular to the lines with direction cosines proportional to 1, -2, -2 and 0, 2, 1.

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l_{1}, m_{1}, n_{1}; l_{2}, m_{2}, n_{2}; l_{3}, m_{3}, n_{3}

are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to

l_{1} + l_{2} + l_{3}, m_{1} + m_{2} + m_{3}, n_{1} + n_{2} + n_{3}

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\frac{2}{3}, - \frac{1}{3}, \frac{2}{3}

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If $l_{1}, m_{1}, n_{1}, l_{2}, m_{2}, n_{2} a n d l_{3}, m_{3}, n_{3}$ are the direction cosines of three mutually perpendicular lines,then prove that the line whose direction cosines are proportional to $l_{1} + l_{2} + l_{3}, m_{1} + m_{2} + m_{3} a n d n_{1} + n_{2} + n_{3}$ makes equal angles with them.

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The direction cosines of the line which is perpendicular to the lines with direction cosines proportional to (1,−2,−2) & (0,2,1) are

The direction cosines of the line which is perpendicular to the lines with direction cosines proportional to $(1, - 2, - 2)$ & $(0, 2, 1)$ are