If the lines r = ( i + m j + 3 k ) + (2 i + 3 j + 4 k ) and r = (4 i + j ) + (5 i + m j + k ) intersect each other, then m =

Step-by-step solution

Equating the position vectors of the two lines for intersection: 1 + 2 = 4 + 5 m + 3 = 1 + m 3 + 4 = From the third equation, = 4 + 3 . Substituting this into the first equation: 2 - 5(4 + 3) = 3 -18 - 15 = 3 -18 = 18 = -1 Substituting = -1 into = 4 + 3 gives = -1 . Now, substituting = -1 and = -1 into the second equation: m + 3(-1) = 1 + m(-1) m - 3 = 1 - m 2m = 4 m = 2 Answer: 2