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For the two lines [0m(x-2)/1 = (y-3)/1 = (z-4)/(-k)[0m and [0m(x-1)/k = (y-4)/2 = (z-5)/1[0m to lie in the same plane, the value of [0m k [0m must be
- k = 3 or -2
- k = 0 or -1
- k = 1 or -1
- k = 0 or -3
Correct answer: k = 0 or -3
Solution
The two lines must be coplanar, which occurs when the scalar triple product of their direction vectors and the vector connecting a point from each line is zero. By calculating the necessary conditions for coplanarity, we find that the values of k that satisfy this condition are 0 or -3.
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