The given point is P(1,2,3). and given line is r=(6
â‹€
i
+7
â‹€
j
+7t
â‹€
k
)+λ(3
â‹€
i
+2
â‹€
j
−2
â‹€
k
) ⇒‌‌‌
x−6
3
=‌
y−7
2
=‌
z−7
−2
=k (say) So, any point on this line is given as Q(3k+6,2k+7,−2k+7) Now, direction ratios of PQ are 3k+5,2k+5,−2k+4 Also, PQ⟂r ‌⇒‌‌3(3k+5)+2(2k+5)−2(−2k+4)=0 ‌⇒‌‌17k+17=0⇒k=−1 Hence, foot of the perpendicular drawn on the given line is (3,5,9).