# TEXAS A&amp;M UNIVERSITY DEPARTMENT OF MATHEMATICS MATH 251-508

```TEXAS A&amp;M UNIVERSITY
DEPARTMENT OF MATHEMATICS
MATH 251-508
Exam 1 version A, 11 Sep 2008
On my honor, as an Aggie, I have neither given nor received unauthorized aid on this work.
Name (print):
In all questions, no analytical work — no points.
1.
Find an equation of the plane that passes through the line of intersections of planes x +
y + z = 1 and 2x − y + z = 3 and passes through the point (1, 1, 2).
2.
Which of the following four lines are parallel? Are any of them identical?
L1 :
L3 :
x = 1 − t, y = 2 + t, z = 3 − 2t
x−3
=y = 2−z
2
r = h4 + 2t, −2t, 2 + 4ti
L4 :
r = h1, −1, 3i + th−2, −1, 1i
L2 :
3.
Find the point of intersection and the angle between the plane x + y + 2z = 6 and the line
x = 1 + 2t, y = 2 − t, z = t.
α
Figure 1: Angle α between a line and a plane
4.
Find an equation for the surface consisting of all points that are equidistant from the point
(−1, 0, 0) and the plane x = 1. Identify and sketch the surface.
5.
(Bonus question +10%) Find the distance from the point (1, 1, 1) to the surface x2 +
y 2 + z 2 + 2x − 6z + 9 = 0.
Points:
/20
```