JEE Main 2022 · 29 Jun · Shift 1 · Mathematics Q23

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MathematicsInteger+4 / -1Question 23 of 90

Let d be the distance between the foot of perpendiculars of the points $P(1,2,-1)$ and $Q(2,-1,3)$ on the plane $-x+y+z=1$ . Then $d^2$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 26

PQ $=(1,-3,4)$ is parallel to the plane ( $\vec{PQ}\cdot(-1,1,1)=0$ ), so the feet are as far apart as P and Q.

$d^2=1+9+16=26$ .

Answer: 26

Topics:Angles and distances

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JEE Main 2022 · 29 Jun · Shift 1, Mathematics question 23