If a line makes an angle of pi /4 with the po | vedclass

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(D) Let the direction cosines of the line be $(l, m, n)$.Given that the line makes an angle of $\alpha = \pi /4$ with the $x$-axis and $\beta = \pi /4

Vedclass · Accepted Answer

$\pi /2$

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(D) Let the direction cosines of the line be $(l, m, n)$.Given that the line makes an angle of $\alpha = \pi /4$ with the $x$-axis and $\beta = \pi /4$ with the $y$-axis.Thus,$l = \cos(\pi /4) = 1/\sqrt{2}$ and $m = \cos(\pi /4) = 1/\sqrt{2}$.We know the identity for direction cosines: $l^2 + m^2 + n^2 = 1$.Substituting the values: $(1/\sqrt{2})^2 + (1/\sqrt{2})^2 + n^2 = 1$.$1/2 + 1/2 + n^2 = 1$.$1 + n^2 = 1 \implies n^2 = 0 \implies n = 0$.If $n = \cos(\gamma) = 0$,then $\gamma = \pi /2$.Therefore,the line makes an angle of $\pi /2$ with the positive direction of the $z$-axis.

If a line makes an angle of $\pi /4$ with the positive direction of both the $x$-axis and $y$-axis,what angle does it make with the positive direction of the $z$-axis?

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