Guys having a problem to find the equation of the line of shortest distance between 2 skew lines. take for an example between ........ x+44=y-2-2=z-30 and x-55=y-33=z0 please show the working.......(ans-x0=y0=z-31)
1The shortest distance will be in the direction perpendicular to both lines. i.e. b1xb2
21Here we require the complete equation of the line,not just its direction cosines.
Get a general pt. on both the lines in terms of λ & μ.
Then find the direction cosine of the line by simply subtracting.
Now the line is perpendicular to both the earlier lines.
Hence by dot product we get 2 equations.
Solve to get 2 pts.Then form the equation of the line.
71Equation of shortest distance line in two plane form :
\begin{vmatrix} x-x_1 &y-y_1 &z-z_1 \\ l_1&m_1 &n_1 \\ l&m &n \end{vmatrix} = 0 = \begin{vmatrix} x-x_2 &y-y_2 &z-z_2 \\ l_2&m_2 &n_2 \\ l&m &n \end{vmatrix}
Where l,m,n are the d.c's of the Shortest distance line found earlier and l1,m1,n1 and l2,m2,n2 are the d.c's of the two lines.
71Practically, there won't be very much difference in the working required. Both forms work very closely along each other.
