Question

A vector is inclined at $\frac{\pi }{4}$ rad with x-axis & $\frac{\pi }{3}$ rad with y-axis then find angle of vector with z-axis.

• A. $\frac{2\pi }{3}$ rad
• B. $\frac{5\pi }{3}$ rad
• C. $\frac{\pi }{4}$ rad
• D. $\frac{\pi }{2}$ rad

Answer 1

Answer: (A)

$\frac{2\pi }{3}$ rad

$co{s}^2\frac{\pi }{4}+{\cos }^2\frac{\pi }{3}+{\cos }^{2}z=1$
${\cos }^{2}z=1-\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$
$\cos z=\pm \frac{1}{2}\Rightarrow z={60}^o,{120}^o\Rightarrow \frac{\pi }{3}$ or $\frac{2\pi }{3}$ rad