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I will use the parametric representation of a line
in 3-dimensions using a vector and a point on the line, to solve
this. There could be other ways.

vector AB = 4 i + 6 j + 2 k vector CD = 7 i - 5 j + 0 k

parametric representation of line AB with point A (0, -1, -1) on it : x = 0 + 4 t , y = -1 + 6 t , z = -1 + 2 t That of line CD is with point C is, x = 3 + 7 s y = 9 - 5 s z = 4 + 0 s Solve these pairs of equations to get t and s. s = -1 , t = 5/2