Problem. Write the equation of the line Delta which parallel to the planes
(P): 3x +12y -3z -5 = 0, (Q): 3x -4y +9z + 7 = 0
and cuts two the lines
(d1): x = 2t -5, y = -4t + 3, z = 3t -1
(d2): x = -2m + 3, y = 3m - 1, z = 4m + 2.
This is my idea.
1) Put A(2t -5, -4t + 3, 3t -1) and B(-2m + 3, 3m - 1, 4m + 2).
2) Find coordinates of vector AB.
3) Because Delta parallel to the planes (P) and (Q), therefore Delta parallel to line of intersection of (P) and (Q). Let v be direction vector of this line. We have AB and v are collinear.
Please help me. Thank you very much.
