JEE Main 2022 · 26 Jun · Shift 2 · Mathematics Q14

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MathematicsSingle correct+4 / -1Question 14 of 90

If the plane $2x+y-5z=0$ is rotated about its line of intersection with the plane $3x-y+4z-7=0$ by an angle of $\dfrac\pi2$ , then the plane after the rotation passes through the point :

(2,-2,0)

(-2,2,0)

(1,0,2)

(-1,0,-2)

Answer and worked solution

Official answer: C

Rotated plane $P_1+\lambda P_2=0$ perpendicular to $P_1$ : $2(2+3\lambda)+(1-\lambda)-5(-5+4\lambda)=30-15\lambda=0$ , so $\lambda=2$ .

Plane. $8x-y+3z-14=0$ .

Check. $(1,0,2)$ : $8+6-14=0$ ✓.

(C)

Topics:Equation of a plane

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JEE Main 2022 · 26 Jun · Shift 2, Mathematics question 14