Mathematics · 2025
JEE Main · 23 January 2025, Shift 2 · Q12
The distance of the line (x-2)/2=(y-6)/3=(z-3)/4 from the point (1,4,0) along the line x/1=(y-2)/2=(z+3)/3 is:
The distance of the line $\displaystyle \frac{x-2}{2}=\frac{y-6}{3}=\frac{z-3}{4}$ from the point $\displaystyle (1,4,0)$ along the line $\displaystyle \frac{x}{1}=\frac{y-2}{2}=\frac{z+3}{3}$ is :
Official answer
From NTA’s final answer key for this paper.
(3)
$\displaystyle \sqrt{14}$
More from 3D Geometry
- 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
- 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
- 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 units from R (1, 2, 3). If (α, β, γ) is…2026
- If the image of the point P(1,0,3) in the line joining the points A(4,7,1) and B(3,5,3) is Q(α, β, γ), then α+β+γ is equal to:2025
- Let in a ABC, the length of the side AC be 6, the vertex B be (1,2,3) and the vertices A, C lie on the line (x-6)/3=(y-7)/2=(z-7)/-2. Then the area…2025
- If the image of the point P(1,2, a) in the line (x-6)/3=(y-7)/2=(7-z)/2 is Q(5, b, c), then a^2+b^2+c^2 is equal to2026
- 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 is 4, then the sum of all possible…2026
JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.