A line AB in three dimensional space marks angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle $\theta $ with the positive z-axis then $\theta $ equals

60°

We have,

$l = cos45°=\frac{1}{\sqrt{2}}, m = cos 120° =-\frac{1}{2}$ and $n = cos \theta $

$∴ l^2 + m^2 + n^2 = 1 $

$⇒ \frac{1}{2}+\frac{1}{4}+cos^2 \theta = 1 ⇒ cos^2\theta = \frac{1}{4}⇒ cos \theta = \frac{1}{2}$  $[∵ \theta $ is acute ]

$⇒ \theta = 60°$