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3-1.Vectors
hard
Vector$\overrightarrow A $ makes equal angles with $x, y$ and $z$ axis. Value of its components (in terms of magnitude of $\overrightarrow A $) will be
A
$\frac{A}{{\sqrt 3 }}$
B
$\frac{A}{{\sqrt 2 }}$
C
$\sqrt 3 \,A$
D
$\frac{{\sqrt 3 }}{A}$
Solution
(a)Let the components of $\overrightarrow A $ makes angles $\alpha ,\,\beta $and $\gamma $ with $x, y$ and $z$ axis respectively then
$\alpha = \beta = \gamma $
${\cos ^2}\alpha + {\cos ^2}\beta + {\cos ^2}\gamma = 1$
$ \Rightarrow $$3{\cos ^2}\alpha = 1$ $ ⇒ \cos \alpha = \frac{1}{{\sqrt 3 }}$
$\therefore \,\,\,{A_x} = {A_y} = {A_z} = A\cos \alpha = \frac{A}{{\sqrt 3 }}$
Standard 11
Physics
