Let given point be P=(1,2,3) and equation of line as
x−6
3
=
y−7
2
=
z−7
−2
=λ (let) ⇒x=3λ+6,y=2λ+7,z=−2λ+7
Coordinates of N=(3λ+6,2λ+7,−2λ+7) .......(i) Since, PN is perpendicular from P on the line AB. Then, direction ratio of PN=3λ+6−1,2λ+7−2,−2λ+7−3 =3λ+5,2λ+5,−2λ+4 and direction ratio of given line =<3,2,−2> ∵PN⊥AB ∴3(3λ+5)+2(2λ+5)+(−2)(−2λ+4)=0[∵a1a2+b1b2+c1c2=0] =9λ+15+4λ+10+4λ−8=0 ⇒ 17λ+17=0 ⇒ λ=−1 Put the value of lambda in Eq. (i), we get =(−3+6,−2+7,2+7)=(3,5,9) Hence, length of perpendicular from the given point.