JEE Main 2022 · 28 Jun · Shift 1 · Mathematics Q16

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MathematicsSingle correct+4 / -1Question 16 of 90

The acute angle between the planes $P_1$ and $P_2$ , when $P_1$ and $P_2$ are the planes passing through the intersection of the planes $5x+8y+13z-29=0$ and $8x-7y+z-20=0$ and the points $(2,1,3)$ and $(0,1,2)$ , respectively, is

\dfrac\pi3

\dfrac\pi4

\dfrac\pi6

\dfrac\pi{12}

Answer and worked solution

Official answer: A

Planes. Through $(2,1,3)$ : $\lambda=\frac72$ , giving $2x-y+z=6$ . Through $(0,1,2)$ : $\lambda=\frac15$ , giving $x+y+2z=5$ .

Angle. $\cos\theta=\dfrac{2-1+2}{\sqrt6\sqrt6}=\frac12$ , so $\frac\pi3$ .

(A)

Topics:Equation of a plane Angles and distances

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JEE Main 2022 · 28 Jun · Shift 1, Mathematics question 16