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Find the direction cosines of a line which makes equal angles with the...

Find the direction cosines of a line whi | Class 12 Mathematics Chapter Three Dimensional Geometry, Three Dimensional Geometry NCERT Solutions

Question:

Find the direction cosines of a line which makes equal angles with the coordinate axes.

Answer:

Let the direction cosines of the line make an angle α with each of the coordinate axes.

∴ l = cos α, m = cos α, n = cos α

l²+m²+n² =1

⇒ cos²α + cos²α + cos²α = 1

⇒ 3cos²α =1

\begin{align}\Rightarrow cos^2α = \frac{1}{3}\end{align}

\begin{align}\Rightarrow cosα = \pm\frac{1}{\sqrt 3}\end{align}

Thus, the direction cosines of the line, which is equally inclined to the coordinate axes, are

\begin{align} \pm\frac{1}{\sqrt 3},\pm\frac{1}{\sqrt 3},and \pm\frac{1}{\sqrt 3}\end{align}

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Comments

Akash
2018-10-27 15:45:44

Nice work.....!

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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , Question 2: Find the direction cosines of a line which makes equal angles with the coordinate axes.....

Find the direction cosines of a line whi | Class 12 Mathematics Chapter Three Dimensional Geometry, Three Dimensional Geometry NCERT Solutions

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