If the angle between the line x=(y-1)/(2)=(z-3)/(lambda) and the plane x+2y+3z=4 is cos^-1 (sqrt((5)/(14)) ) , then lambda equals :

3D Geometry: If the angle between the line x=(y-1)/(2)=(z-3)/(lambda) and the… | AIEEE 2011

AIEEE 2011 (Offline)Question 1

If the angle between the line $x=\frac{y-1}{2}=\frac{z-3}{\lambda}$ and the plane $x+2y+3z=4$ is $\cos^{-1}\left(\sqrt{\frac{5}{14}}\right)$, then $\lambda$ equals :

3D Geometry

$\frac32$$\frac25$$\frac53$$\frac23$✓ Correct answer

Solution

$\cos\theta=\sqrt{\frac5{14}}\Rightarrow\sin\theta=\frac3{\sqrt{14}}=\frac{|1+4+3\lambda|}{\sqrt{5+\lambda^2}\sqrt{14}}$, so $(5+3\lambda)^2=9(5+\lambda^2)$, $\lambda=\frac23$.

3D Geometry - JEE Mathematics question (AIEEE 2011 (Offline))

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