jee-main 2022 Q78

jee-main · India · session2_25jul_shift2 Vectors 3D & Lines Normal Vector and Plane Equation

A plane $E$ is perpendicular to the two planes $2x - 2y + z = 0$ and $x - y + 2z = 4$, and passes through the point $P(1, -1, 1)$. If the distance of the plane $E$ from the point $Q(a, a, 2)$ is $3\sqrt{2}$, then $(PQ)^2$ is equal to
(1) 9
(2) 12
(3) 21
(4) 33

A plane $E$ is perpendicular to the two planes $2x - 2y + z = 0$ and $x - y + 2z = 4$, and passes through the point $P(1, -1, 1)$. If the distance of the plane $E$ from the point $Q(a, a, 2)$ is $3\sqrt{2}$, then $(PQ)^2$ is equal to\\
(1) 9\\
(2) 12\\
(3) 21\\
(4) 33

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