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(B) The direction cosines of a line are defined as $l = \cos \alpha$,$m = \cos \beta$,and $n = \cos \gamma$,where $\alpha, \beta, \gamma$ are the angl

Vedclass · Accepted Answer

$\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$

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(B) The direction cosines of a line are defined as $l = \cos \alpha$,$m = \cos \beta$,and $n = \cos \gamma$,where $\alpha, \beta, \gamma$ are the angles made by the line with the $x, y,$ and $z$ axes respectively. It is a fundamental property in three-dimensional geometry that the sum of the squares of the direction cosines is always equal to $1$. Therefore,$l^2 + m^2 + n^2 = 1$. Substituting the values of $l, m,$ and $n$,we get $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.

If $\alpha, \beta, \gamma$ are the angles that a line makes with the coordinate axes,then which of the following is true?

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