Class 12 Mathematics - Chapter Three Dimensional Geometry NCERT Solutions | Find the direction cosines of a line whi
Find the direction cosines of a line which makes equal angles with the coordinate axes.
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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Nice work.....!
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