JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q84

← JEE Main 2014 · 19 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 84 of 90

If the angle between the line $2(x+1)=y=z+4$ and the plane $2x-y+\sqrt\lambda z+4=0$ is $\dfrac\pi6$ , then the value of λ is :

\dfrac{135}7

\dfrac{45}{11}

\dfrac{45}7

\dfrac{135}{11}

Answer and worked solution

Official answer: C

The line $2(x+1)=y=z+4$ has direction $(1,2,2)$ , $|{\cdot}|=3$ . The plane's normal is $(2,-1,\sqrt\lambda)$ .
$\sin\frac\pi6=\frac{|2-2+2\sqrt\lambda|}{3\sqrt{5+\lambda}}=\frac12\implies16\lambda=9(5+\lambda)\implies\lambda=\frac{45}7.$

Topics:Angles and distances

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JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 84