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 $
$\Rightarrow \theta = 90^{\circ}$