00:01
In this question, we are asked to find parametric equations of the line parallel to the z -axis and passing through the midpoint of the point 0 -4 -5 and negative 6 -5 -3.
00:17
The general vector equation of the line is going to be r of t equals to x -not, y -not, z -not, plus t multiplied by v.
00:30
Where x, y, knot and z knot are coordinates of any point lying on the line.
00:39
And we can take that to be the midpoint or the given two points.
00:46
And v is any vector parallel to our line.
00:51
And recall that our line is parallel to z -axis.
00:55
So basically, v could be any vector parallel to the z -axis.
01:04
All right.
01:05
One vector parallel to the z -axis is the, vector 0 -01.
01:16
Recall that if we draw the xy z plane, sorry xy z coordinate system, this is the x -axis, this is a y -axis, and this is a z -axis.
01:35
And the vector going up in the positive z direction has coordinates and of length 1 has coordinates 0 ,0.
01:44
So it's parallel to the x axis.
01:52
And since it's parallel to the z -axis, and our line is parallel to the x -axis, it's parallel to our line...