Question
The general equation of the plane through a line is given by (3+k)x + (2-3k)y + z(1+2k) -2-13k, for some integer k
How do we find the equation of the line containing above and parallel to the line given by,
(x+5)/3 = (y+4)/1 = (z-7)/-2
My initial thought was to take proportions of the two lines' direction ratios, but instead the answer given by the professor has multiplied the direction ratios and then their sums has been equated to zero, as in,
3(3+k) + 1(2-3k)y - 2(1+2k) = 0
Can I know the reason for that?
How do we find the equation of the line containing above and parallel to the line given by,
(x+5)/3 = (y+4)/1 = (z-7)/-2
My initial thought was to take proportions of the two lines' direction ratios, but instead the answer given by the professor has multiplied the direction ratios and then their sums has been equated to zero, as in,
3(3+k) + 1(2-3k)y - 2(1+2k) = 0
Can I know the reason for that?