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