0
$\begingroup$

My question is : how can i prove if a line r in 3D In parametric form is skew with the z-axis Knowing that the line r for example has equation : $$ \left\{ \begin{array}{c} X=1+t \\ Y=2-t\\ Z=1+t\end{array} \right. $$ I tried to prove that the cross product of the direction vector of r and z-axis is different from zero (not parallel) and the dot product also different then zero ( not perpendicular) but what about the intersection between them ?

$\endgroup$
3
$\begingroup$

The line intersects the z-axis if $X=Y=0$. But that is impossible in your case.

To check that the line is not parallel to the z-axis, just notice that its direction vector $(1,-1,1)$ is not a multiple of $(0,0,1)$.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

The lines are parallel if their direction vector are the multiple of each other (or the same), meanwhile if it's not it can be either intersecting or skew. They are skew if you cant find the intersection point of those two line

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.