If the foot of the perpendicular drawn from the point (1,0,3) on a line passing through (α,7,1) is (35,37,317), then α is equal to \_\_\_\_\_\_\_.
Answer: 4
Solutions · 1
Official solution
Let F=(35,37,317). Line direction =F−(α,7,1)=(35−α,−314,314); PF=F−(1,0,3)=(32,37,38) must be perpendicular to this direction:
\[\tfrac23\left(\tfrac53-\alpha\right)-\tfrac{98}9+\tfrac{112}9=0\implies \tfrac23\left(\tfrac53-\alpha\right)=-\tfrac{14}9\implies \tfrac53-\alpha=-\tfrac73\implies\alpha=4.\]