Mathematics · 2023
JEE Main · 11 April 2023, Shift 1 · Q8
If equation of the plane that contains the point (-2,3,5) and is perpendicular to each of the planes 2 x+4 y+5 z=8 and 3 x-2 y+3 z=5 is α x+β y+γ…
If equation of the plane that contains the point $\displaystyle (-2,3,5)$ and is perpendicular to each of the planes $\displaystyle 2 x+4 y+5 z=8$ and $\displaystyle 3 x-2 y+3 z=5$ is $\displaystyle \alpha x+\beta y+\gamma z+97=0$ then $\displaystyle \alpha+\beta+\gamma=$
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle 15$
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
- 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 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
- Let the image of the point (1,0,7) in the line x/1=(y-1)/2=(z-2)/3 be the point (α, β, γ). Then which one of the following points lies on the line…2024
- Consider the lines L_1 and L_2 given by L_1: (x-1)/2=(y-3)/1=(z-2)/2; L_2: (x-2)/1=(y-2)/2=(z-3)/3. A line L_3 having direction ratios 1,-1,-2,…2023
- Let the plane containing the line of intersection of the planes P 1: x+(λ+4) y+z=1 and P 2: 2 x+ y+z=2 pass through the points (0,1,0) and (1,0,1).…2023
- The sum of all values of α, for which the shortest distance between the lines (x+1)/(α)=(y-2)/-1=(z-4)/(-α) and x/(α)=(y-1)/2=(z-1)/(2 α) is √2, is2026
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.