Let P(1,2,3) and Q(α,β,γ), where Q is foot of perpendicular to the line
x−2
4
=
y−3
5
=
z−4
6
=λ from P
Now, coordinates of Q are (4λ+2,5λ+3,6λ+4) ∴DR′s of line joining PQ are <4λ+2−1,5λ+3−2,6λ+4−3> i.e., <4λ+1,5λ+1,6λ+1> Again PQ is perpendicular to the given line, so 4(4λ+1)+5(5λ+1)+6(6λ+1)=0 ⇒16λ+4+25λ+5+36λ+6=0 ⇒77λ=−15⇒λ=