Question

If a line makes angles $35^{\circ }$ and $55^{\circ }$ with x-axis and y-axis respectively, then the angle which this line subtends with z-axis is:

• A. $35^{\circ }$
• B. $45^{\circ }$
• C. $55^{\circ }$
• D. $90^{\circ }$

Answer 1

Answer: (D)

As given : Line makes an angle $35^{\circ }$ with x-axis and $55^{\circ }$ with y-axis and
Let angle $\theta$ with z-axis
From property of direction cosines,
${\cos }^{2}35+{\cos }^{2}55+{\cos }^2\theta =1$
$\Rightarrow {\cos }^2(\pi /2-55)+{\cos }^{2}55+{\cos }^2\theta =1$
$\Rightarrow {\sin }^{2}55+{\cos }^{2}55+{\cos }^2\theta =1$
$\Rightarrow 1+{\cos }^2\theta =1$
$\Rightarrow {\cos }^2\theta =0$
$\Rightarrow \theta =90^{\circ }$