Equation Of A Line In Space

Step 1: Use the section formula.
To find the point of intersection with the -plane, substitute into the equation of the line joining and .
Step 2: Conclusion.
The coordinates of the point of intersection with the -plane are . Final Answer:

The given system of lines passes through the point of intersection of the straight lines and form which is .
The required line will also pass through this point.
Further, the line will be farthest from point
if it is in direction perpendicular to line joining and .
The equation of the required line is

Direction vectors: vecAB=(k,-1,3), vecBC=(2,k,-1) Perpendicular ⟹ vecAB·vecBC=0: 2k-k-3=0⟹ k=3