JEE Main 2022 · 25 Jul · Shift 1 · Mathematics Q14

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MathematicsSingle correct+4 / -1Question 14 of 90

Let P be the plane containing the straight line $\dfrac{x-3}9=\dfrac{y+4}{-1}=\dfrac{z-7}{-5}$ and perpendicular to the plane containing the straight lines $\dfrac x2=\dfrac y3=\dfrac z5$ and $\dfrac x3=\dfrac y7=\dfrac z8$ . If d is the distance of P from the point $(2,-5,11)$ , then $d^2$ is equal to :

\dfrac{147}2

\dfrac{32}3

Answer and worked solution

Official answer: C

Normals. Second plane: $(2,3,5)\times(3,7,8)=(-11,-1,5)$ . P contains $(9,-1,-5)$ and that normal: $n=(9,-1,-5)\times(-11,-1,5)$ , through $(3,-4,7)$ .

Distance of $(2,-5,11)$ : $d^2=\frac{32}3$ .

(C)

Topics:Equation of a plane Angles and distances

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JEE Main 2022 · 25 Jul · Shift 1, Mathematics question 14