Mathematics · 2024
JEE Main · 30 January 2024, Shift 1 · Q16
Let (α, β, γ) be the foot of perpendicular from the point (1,2,3) on the line (x+3)/5=(y-1)/2=(z+4)/3. Then 19(α+β+γ) is equal to:
Let $\displaystyle (\alpha, \beta, \gamma)$ be the foot of perpendicular from the point $\displaystyle (1,2,3)$ on the line $\displaystyle \frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$. Then $\displaystyle 19(\alpha+\beta+\gamma)$ is equal to :
Official answer
From NTA’s final answer key for this paper.
(3)
$\displaystyle 101$
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
- 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
- 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 the point (-1, α, β) lie on the line of the shortest distance between the lines (x+2)/-3=(y-2)/4=(z-5)/2 and (x+2)/-1=(y+6)/2=(z-1)/0. Then…2024
- 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
JEE Main 2024 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.