JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 26 February 2021, Shift 1, Maths Q87

Question 87 of 90 in this shift, Maths question 27 of 30, Section B.

Let

(\lambda, 2, 1)

be a point on the plane which passes through the point

(4, -2, 2)

. If the plane is perpendicular to the line joining the points

(-2, -21, 29)

and

(-1, -16, 23)

, then

\left(\frac{\lambda}{11}\right)^2-\frac{4\lambda}{11}-4

is equal to _________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Normal and Point Form

Same topic in other shifts

All Planes in 3D questions

6 Apr 2023, Shift 1 · Q13If the equation of the plane passing through the line of intersection of the planes $2x-y+z=3$ , $4x-3y+5z+9=0$ and parallel to the line…MediumSingle correct
6 Apr 2023, Shift 1 · Q30Let the image of the point $(1,2,3)$ in the plane $2x-y+z=9$ be Q. If the coordinates of the point R are $(6,10,7)$ , then the square of…MediumNumerical value
6 Apr 2023, Shift 2 · Q15A plane P contains the line of intersection of the plane $\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=6$ and…MediumSingle correct
8 Apr 2023, Shift 1 · Q15If the equation of the plane containing the line $x+2y+3z-4=0=2x+y-z+5$ and perpendicular to the plane…MediumSingle correct
8 Apr 2023, Shift 2 · Q13Let $P$ be the plane passing through the line $\frac{x-1}{1} = \frac{y-2}{-3} = \frac{z+5}{7}$ and the point $(2, 4, -3)$ . If the image of…MediumSingle correct
8 Apr 2023, Shift 2 · Q14For $a, b \in \mathbb{Z}$ and $|a - b| \leq 10$ , let the angle between the plane $P: ax + y - z = b$ and the line…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.