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Class 12
Mathematics
Three Dimensional Geometry
find the direction cosines of a line which makes e...

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

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