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(A) Let the components of $\overrightarrow{A}$ make angles $\alpha, \beta,$ and $\gamma$ with the $x, y,$ and $z$ axes respectively.Given that the vec

Vedclass · Accepted Answer

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

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(A) Let the components of $\overrightarrow{A}$ make angles $\alpha, \beta,$ and $\gamma$ with the $x, y,$ and $z$ axes respectively.Given that the vector makes equal angles with all axes,we have $\alpha = \beta = \gamma$.The direction cosines 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 are given by $A_x = A \cos \alpha$,$A_y = A \cos \beta$,and $A_z = A \cos \gamma$.Therefore,$A_x = A_y = A_z = A \left( \frac{1}{\sqrt{3}} \right) = \frac{A}{\sqrt{3}}$.

Vector $\overrightarrow{A}$ makes equal angles with $x, y,$ and $z$ axes. The value of its components (in terms of the magnitude of $\overrightarrow{A}$) will be:

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