Question

If theta is the angle between $\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$ and the plane $2x-y+\sqrt{\lambda z}+4=0$ and is such that sin(theta) $=\frac{1}{3}$, the value of $\lambda =$

• A. $-\frac{4}{3}$
• B. $\frac{4}{3}$
• C. $-\frac{3}{5}$
• D. $\frac{5}{3}$

Answer 1

The correct option is D $\frac{5}{3}$

$Sin\theta =\left|\frac{2-2+2\sqrt{\lambda }}{3\sqrt{5+\lambda }}\right|=\frac{1}{3}\lambda =\frac{5}{3}$