[9.5] - Reading Questions

Read section 9.5 in the textbook.

1. When specifying the equation of a line in space, the text says that you need a point on the line and a vector parallel to the line. Why can’t you determine a line in space simply by using one vector?

   Except for a position vector (tail always goes at the origin), a vector is only defined by its length and direction, and not its position in space.

2. Find three "parametric equations" of the line passing through the points (1,2,1) and (-1,3,5).

   
   

   Other equations are possible, for example: $$\frac{x-1}{2}=\frac{y-2}{-1}=\frac{z-1}{-4}.$$

3. What's one or two "muddy points" in the reading that you'd like to clear up? Or (if nothing seemed muddy) one thing that you *wonder* about?