Let L be the foot of perpendicular drawn from the point P(1,2,3) to the given line. The coordinate of a general point on ‌
x−6
3
=‌
y−7
2
=‌
z−7
−2
=λ are given by (3λ+6,2λ+7,−2λ+7) Let this point be L.
Now, direction ratios of PL are ‌3λ+6−1,2λ+7−2,−2λ+7−3 ‌ i.e., ‌‌3λ+5,2λ+5,−2λ+4 and direction cosines of given line are 3,2,−2. ∵PL is perpendicular to the given line. ∴ 3(3λ+5)+2(2λ+5)+(−2)(−2λ+4)=0 ⇒‌‌λ=−1 ∴‌‌L(3×−1+6,2×−1+7,−2×−1+7) ‌‌=L(3,5,9) ∴‌‌PL=√(3−1)2+(5−2)2+(9−3)2 ‌‌=7 units