Line: r=(−1,3,1)+λ(2,3,−1), Point P = (5, 4, 2).
Any point on line: Q=(−1+2λ,3+3λ,1−λ).
PQ=(−6+2λ,−1+3λ,−1−λ).
For perpendicular: PQ⋅(2,3,−1)=0 gives 14λ−14=0, so λ=1.
Foot (α,β,γ)=(1,6,0).
Projection of (1,6,0) on (6,2,3): 49∣6+12+0∣=718.
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^+3j^+k^)+λ(2i^+3j^−k^).
Then the length of the projection of the vector αi^+βj^+γk^ on the vector 6i^+2j^+3k^ is :
Held on 21 Jan 2026 · Verified 6 Jul 2026.
715
4
718
3
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