Consider any line in space that does not pass through the origin.

a. Is it possible for this line to intersect just one coordinate axis? exactly two? all three? none at all?

b. Is it possible for this line to intersect just one coordinate plane? exactly two? all three? none at all?

Find a vector equation of the line

that passes through the points \displaystyle (3,9) and \displaystyle (-4,2)

Find a vector equation of the line

that passes through the point \displaystyle (-5,-3) and is parallel to the line \displaystyle \vec{r}=(4,0)+t(0,5)

Find a vector equation of the line

that is perpendicular to the line \displaystyle 2 x-5 y-6=0 and passes through the point \displaystyle (0,-3)

Determine if the following pairs of lines are parallel and distinct, coincident, perpendicular, or none of these.

\displaystyle (x, y, z)=(1,7,2)+t(-1,-1,1) and \displaystyle (x, y, z)=(-3,0,1)+u(2,-2,-2)

At what points does the line \displaystyle \frac{x+4}{2}=\frac{y-6}{-1}=\frac{z+2}{4} meet the coordinate planes?

Find the coordinates of the foot of the perpendicular from \displaystyle Q(3,2,4) to the line \displaystyle \vec{r}=(-6,-7,-3)+t(5,3,4)