Math 2414
Homework Set 10
10 Points
The 3-D Coordinate System
1. Find the distance from the point (-1, 5, 3) to
(a) the xy-plane
(b) the xz-plane
(c) the x-axis
2. Sketch the graph of y 2 + z 2 =
9 in  2 and  3 .
Equations of Lines
For problems 3 & 4 give the vector and parametric form of the equation of given line.
3. The line that passes through (10, 4, -1) and (-3, 5, -2).
3 − 2t , y =
9 t, z =
1 + 21t .
4. The line that passes through (0, 4, 1) and is parallel to x =

5. Determine if the two lines x =
4 − 3t , y =
8, z =
2 + 17t and r ( t ) = 8 − 3t , 7 + t ,3 + 5t are
orthogonal, parallel or neither.
Equations of Planes
For problems 6 & 7 find the equation of the given plane.
6. The plane containing (1, -2, 3), (0, 5, -1) and (4, 0, -2).

7. The plane containing r ( t ) =
3 + 5t ,1 − 6t , −7 + 2t and is parallel to −2 x + y + 8 z =
1.
Quadric Surfaces
For problems 8 & 9 sketch the surface. I’m not after a picture perfect sketch here. Your sketch should
be recognizable as the proper type of surface that has the correct orientation along the correct axis and
be in the proper place on the correct axis.
8. y =14 − 3 x 2 − 3 z 2
9. =
x2 2 y 2 + 2z 2