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If a line $\overline {AB}$ makes angle $45^{\circ}$ with positive $x-axis$ and $120^{\circ}$ with positive $y-axis$, then the angle $\theta$ made by the line with positive $z-axis$ is ?


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  • If a line makes angles $\theta_1,\theta_2,\theta_3$ respectively with positive coordinate axes, then $cos^2 \theta_1+cos^2 \theta_2+cos^2 \theta_3=1$
Since it is given that $\overline {AB}$ makes $45^{\circ},\:120^{\circ}\:and\:\:\theta$ with the coordinate axes,
$cos^2 45^{\circ}+cos^2 120^{\circ}+cos^2 \theta=1$
answered Dec 27, 2013 by rvidyagovindarajan_1

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