A vector overrightarrow{A} makes equal angles | vedclass

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(A) Let the angles made by the vector $\overrightarrow{A}$ with the $x$,$y$,and $z$ axes be $\alpha$,$\beta$,and $\gamma$ respectively.Given that the

Vedclass · Accepted Answer

$\frac{A}{\sqrt{3}}$

Vedclass · Answer

(A) Let the angles made by the vector $\overrightarrow{A}$ with the $x$,$y$,and $z$ axes be $\alpha$,$\beta$,and $\gamma$ respectively.Given that the vector makes equal angles with the axes,we have $\alpha = \beta = \gamma$.The direction cosines of the vector satisfy the relation $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.Substituting $\alpha = \beta = \gamma$,we get $3 \cos^2 \alpha = 1$,which implies $\cos \alpha = \frac{1}{\sqrt{3}}$.The components of the vector $\overrightarrow{A}$ are given by $A_x = A \cos \alpha$,$A_y = A \cos \beta$,and $A_z = A \cos \gamma$.Therefore,$A_x = A_y = A_z = A \left( \frac{1}{\sqrt{3}} \right) = \frac{A}{\sqrt{3}}$.

$A$ vector $\overrightarrow{A}$ makes equal angles with the $x$,$y$,and $z$ axes. Find the magnitude of its components.

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