It is given that
Line joining O (0, 0, 0) and A (2, 1, 1) is written as
OA = 2i + j + k
Line joining B (3, 5, -1) and D (4, 3, -1) is written as
BC = i – 2j + 0k
In order prove that these two lines are perpendicular we must show that angle between these two lines is π/2
Dot product OA . BC = 0
Substituting the values
(2i + j + k). (i – 2j + 0k) = 2 – 2 + 0 = 0
Hence, these two lines are perpendicular.