VITEEE 2014 Paper

Vertices of ΔABC are A (0,4,1), B (2,3,-1) and C (4,5,0).
AB = √(2−0)2+(3−4)2+(−1−1)2 = √4+1+4 = 3
BC = √(4−2)2+(5−3)2+(0+1)2 = √4+4+1 = 3
and CA = √(4−0)2+(5−4)2+(0−1)2
= √16+1+1 = 3√2
AB2+BC2 = AC2
∴ Δ ABC is a right angled triangle.
We know that, the orthocentre of a right angled triangle is the vertex containing the right angle.
∴ Orthocentre is point B (2, 3,-1).