Mathematics · 2026
JEE Main · 2 April 2026, Shift 2 · Q15
Let the point A be the foot of perpendicular drawn from the point P ( a, b, 0) on the line (x-1)/2=(y-2)/1=(z-α)/3. If the midpoint of the line…
Let the point A be the foot of perpendicular drawn from the point $\displaystyle \mathrm{P}(\mathrm{a}, \mathrm{b}, 0)$ on the line $\displaystyle \frac{x-1}{2}=\frac{y-2}{1}=\frac{z-\alpha}{3}$. If the midpoint of the line segment PA is $\displaystyle \left(0, \frac{3}{4}, \frac{-1}{4}\right)$, then the value of $\displaystyle \mathrm{a}^2+\mathrm{b}^2+\alpha^2$ is equal to :
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle 1$
More from 3D Geometry
- Let a triangle PQR be such that P and Q lie on the line (x+3)/8=(y-4)/2=(z+1)/2 and are at a distance of 6…2026
- If the distance of the point (a, 2, 5) from the image of the point (1, 2, 7) in the line x/1=(y-1)/1=(z-2)/2…2026
- Let a line L be perpendicular to both the lines L_1: (x+1)/3=(y+3)/5=(z+5)/7 and L_2:…2026
- Let the image of the point P(0,-5,0) in the line (x-1)/2=y/1=(z+1)/-2 be the point R and the image of the…2026
- Let a line L_1 pass through the origin and be perpendicular to the lines L_2: r=(3+t) i+(2 t-1) j+(2 t+4) k…2026
- Let the foot of perpendicular from the point (λ, 2,3) on the line (x-4)/1=(y-9)/2=(z-5)/1 be the point (1, μ,…2026
- Let the image of the point P(1,6, a) in the line L: x/1=(y-1)/2=(z-a+1)/b, b>0, be (a/3, 0, a+c). If S(α, β,…2026
- If (2 α+1, α^2-3 α, (α-1)/2) is the image of (α, 2 α, 1) in the line (x-2)/3=(y-1)/2=z/1, then the possible…2026
JEE Main 2026 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.