If the shortest distance between the line joining the points (1,2,3) and (2,3,4), and the line 2x−1=−1y+1=0z−2 is α, then 28α2 is equal to:
Answer: 18
Solutions · 1
Official solution
Point A(1,2,3), direction (1,1,1); point B(1,−1,2), direction (2,−1,0).
\[(1,1,1)\times(2,-1,0)=(1,2,-3),\qquad |(1,2,-3)|=\sqrt{14}.\]
\[\vec{AB}=(0,-3,-1),\qquad \vec{AB}\cdot(1,2,-3)=0-6+3=-3.\]
\[\alpha=\frac{3}{\sqrt{14}} \implies \alpha^2=\frac{9}{14} \implies 28\alpha^2=18.\]