1. Using the sketch below, come up with a plan to find the distance between a plane and a point not on the plane.
2. Now, use your plan to find the distance between the plane 5x + y - z = 1 and the point (2,4,-1).
3. Explain how your plan be expanded to find the distance between a plane and a line which does not intersect the plane.
4. Find the distance between the two parallel planes : 5x + y - z = 1 and 10* + 2y - 2z = 5. You should be able to use your plan above to help with this one. (Also, think about how you know these two planes are parallel.)
5. Skew lines are lines in space which are not parallel but also do not intersect. Come up with a plan to find the distance between two skew lines if you know a point on each line and a vector parallel to each line. Then use your plan to find the distance between the two lines given the following:
- (1, -2, 4) is a point on the line one and vector v bar = i^ + 3j^-k^ is parallel to this line
- (0, 3, -3) is a point on line two and vector w bar = 2i^ + j^ + 4k^ is parallel to this line.