JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q17

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MathematicsSingle correct+4 / -1Question 17 of 90

If the plane P passes through the intersection of two mutually perpendicular planes $2x+ky-5z=1$ and $3kx-ky+z=5$ , $k<3$ and intercepts a unit length on positive $x$ -axis, then the intercept made by the plane P on the $y$ -axis is

\dfrac1{11}

\dfrac5{11}

Answer and worked solution

Official answer: D

Perpendicular planes. $6k-k^2-5=0$ gives $k=1$ (as $k<3$ ).

Plane P. $(2x+y-5z-1)+\lambda(3x-y+z-5)=0$ with $x$ -intercept 1 gives $\lambda=\frac12$ : $7x+y-9z=7$ .

$y$ -intercept 7. (D)

Topics:Equation of a plane

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JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 17