Vector \vec{A} makes equal angles with x,y and z axis. Value of its components (in terms of magnitude of \vec{A} ) will be
\((a) \frac{A}{\sqrt{3}}
(b) \frac{A}{\sqrt{2}}
(c) \sqrt{3} A
(d) \frac{\sqrt{3}}{A}\)
Text Solution
Verified by ExpertsA
Let the components of \vec{A} makes angles \(\alpha, \beta\) and \(\gamma\) with x, y and z axis respectively then \(\alpha = \beta = \gamma\)
\(\cos^{2} \alpha + \cos^{2} \beta + \cos^{2} \gamma = 1\)
\(\Rightarrow 3 \cos^{2} \alpha = 1 \Rightarrow \cos \alpha = \frac{1}{\sqrt{3}}\)
\(\therefore A_x = A_y = A_z = A \cos \alpha = \frac{A}{\sqrt{3}}\)
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