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# What are the d . c . s of the vector equally inclined to the axes?

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• If $l, m , n$ are the d.c.s of a vector, then $l^2+m^2+n^2=1$
Let $l, m, n$ be the D.c.s of a vector that is equally inclined to the axes.
$\therefore \: l = m = n$
$l^2+m^2+n^2=1 \Rightarrow 3l^2=1\: \: or \: l= \pm \large\frac{1}{\sqrt 3}$
$\therefore$ the D.c.s are $\large\frac{1}{\sqrt 3}, \large\frac{1}{\sqrt 3}, \large\frac{1}{\sqrt 3}\: or \: -\large\frac{1}{\sqrt 3}, -\large\frac{1}{\sqrt 3}, -\large\frac{1}{\sqrt 3}$

edited Jun 24, 2013

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