1. ## Parametric equation

Find parametric equations for the line through the point(0,1,2) that is perpendicular to the line x=1+t, y=1-t, z=2t and intersects this line.

I am wondering that intersects what line.

Does this question give enough information for calculating?

If yes, how can I calculate it.

2. Find parametric equations for the line through the point(0,1,2) that is perpendicular to the line x=1+t, y=1-t, z=2t and intersects this line.

"this line" refers to the line given parametrically by x=1+t, y=1-t, z=2t.

Otherwise, the problem would have been asking you to find a line that intersects itself, which is stupid. Still, as it is now, the "and intersects this line" bit is redundant/useless information (since by definition, two perpendicular lines INTERSECT to form a 90 degree angle).

Rewrite the problem lopping off the last 4 words, i.e.,
Find parametric equations for the line through the point(0,1,2) that is perpendicular to the line x=1+t, y=1-t, z=2t.

3. Now does this problem make sense? If not, we can get into that.
-Andy