Answer :

Given: A(3, 5, -1) and B(5, p, 0)


The line joining these two points is given by,


AB = 2i + (p-5)j + k


C(2, 1, 1) and D(3, 3, -1),


The line joining these two points,


CD = i + 2j - 2k


As the two lines are perpendicular, we know that the angle between these two lines is


So, AB.CD = 0 (dot product)


Thus, (2i + (p-5)j + k) .(i + 2j - 2k) = 0.


ð


ð p = 5


Thus, p = 5.


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