Q6 of 26 Page 1

If the lines and are perpendicular to each other, then find the value of p.

Equation of lines in 3D are

Line I:



Line II:



Since the lines are perpendicular therefore the dot product of the direction cosines should be 0


Here,


l1 = –2; m1 = 3p; n1 = 4 & l2 = 4p; m2 = 2; n2 = –7


l1 × l2 + m1 × m2 +n1 × n2 = 0


–2 × 4p + 3p × 2 + 4 × (–7) = 0


–8p + 6p = 28


2p = –28


p = –14


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