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Write the Angle Between the Lines Whose Direction Ratios Are Proportional to 1, −2, 1 and 4, 3, 2. - CBSE (Arts) Class 12 - Mathematics

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Question

Write the angle between the lines whose direction ratios are proportional to 1, −2, 1 and 4, 3, 2.

Solution

\[ \text{ The direction ratios of the first line are 1, - 2, 1 and the direction ratios of the second line are 4, 3, 2 } . \]

\[ \text{ Let } \theta \text{ be the angle between these two lines } . \]

\[\text{ Now }, \]

\[\cos \theta = \left| \frac{1\left( 4 \right) + \left( - 2 \right)\left( 3 \right) + 1\left( 2 \right)}{\sqrt{\left( 1 \right)^2 + \left( - 2 \right)^2 + \left( 1 \right)^2} \sqrt{\left( 4 \right)^2 + \left( 3 \right)^2 + \left( 2 \right)^2}} \right|\]

\[ = \left| \frac{4 - 6 + 2}{\sqrt{1 + 4 + 1}\sqrt{16 + 9 + 4}} \right|\]

\[ = \frac{0}{\sqrt{6}\sqrt{29}}\]

\[ = 0 \]

\[ \Rightarrow \theta = \frac{\pi}{2}\]

\[\text { Hence, the required angle is } \frac{\pi}{2} .\]

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (2018 to Current)
Chapter 27: Direction Cosines and Direction Ratios
Ex.Very Short Answers | Q: 12 | Page no. 25
Solution Write the Angle Between the Lines Whose Direction Ratios Are Proportional to 1, −2, 1 and 4, 3, 2. Concept: Direction Cosines and Direction Ratios of a Line.
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