Mathematics · 2022
JEE Main · 26 June 2022, Shift 1 · Q15
Let the plane 2 x+3 y+z+20=0 be rotated through a right angle about its line of intersection with the plane x-3 y+5 z=8. If the mirror image of the…
Let the plane $\displaystyle 2 x+3 y+z+20=0$ be rotated through a right angle about its line of intersection with the plane $\displaystyle x-3 y+5 z=8$. If the mirror image of the point $\displaystyle \left(2,-\frac{1}{2}, 2\right)$ in the rotated plane is $\displaystyle \mathrm{B}(\mathrm{a}, \mathrm{b}, \mathrm{c})$, then :
Official answer
(1)
$\displaystyle \frac{a}{8}=\frac{b}{5}=\frac{c}{-4}$
More from 3D Geometry
- If the foot of the perpendicular drawn from (1, 9, 7) to the line passing through the point (3,2,1) and parallel to the planes x+2 y+z=0 and 3 y-z=3…2023
- Let a x+b y+c z+3=0 be the plane which bisects the acute angle between the planes 2 x-y-2 z+3=0 and 3 x-2 y+6 z+8=0. Then a+b+c is equal to2022
- Let the plane passing through the point (-1, 0, -2) and perpendicular to each of the planes 2 x+y-z=2 and x-y-z=3 be a x+b y+c z+8=0. Then the value…2021
- The shortest distance between the lines (x-4)/4=(y+2)/5=(z+3)/3 and (x-1)/3=(y-3)/4=(z-4)/2 is2023
- Let the values of p, for which the shortest distance between the lines (x+1)/3=y/4=z/5 and r=(p i+2 j+ k)+λ(2 i+3 j+4 k) is 1/(√6), be a, b, (a < b).…2025
- Let the mirror image of the point ( a, b, c ) with respect to the plane 3 x-4 y+12 z+19=0 be (a-6, β, γ). If a+b+c=5, then 7 β-9 γ is equal to \ \ \…2022
- Let a line pass through two distinct points P(-2,-1,3) and Q, and be parallel to the vector 3 i+2 j+2 k. If the distance of the point Q from the…2025
- The plane passing through the points (1,2,1),(2,1,2) and parallel to the line, 2 x=3 y, z=1 also passes through the point:2020
JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.