Let (α,β,γ) be the co-ordinates of the foot of the perpendicular drawn from the point (5,4,2) on the line r=(- i+3 j+ k)+λ(2 i+3 j- k). Then the length of the projection of the vector α i+β j+γ k on the vector 6 i+2 j+3 k is:

Three Dimensional Geometry: JEE Main 2026 Mathematics question

JEE Main 2026 · 21 Jan, Morning shift · Q20

JEE Main 202621 Jan, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let

(\alpha,\beta,\gamma)

be the co-ordinates of the foot of the perpendicular drawn from the point

(5,4,2)

on the line

\vec r=(-\hat i+3\hat j+\hat k)+\lambda(2\hat i+3\hat j-\hat k)

. Then the length of the projection of the vector

\alpha\hat i+\beta\hat j+\gamma\hat k

on the vector

6\hat i+2\hat j+3\hat k

is :