TEXAS A&M UNIVERSITY
DEPARTMENT OF MATHEMATICS
MATH 251-509
Exam 1 version A, 31 Jan 2008
Name:
Points:
In all questions, no analytical work — no points.
1.
Find the parametric equation of the intersection of two planes:
x−y−z = 0
and
2x + y + 2z = 3.
/20
2.
Find the equation of the plane which contains the points A(1, 1, 0) and B(1, 2, −1) and
which does not intersect the line x = 1 + t, y = 2t, z = −1 + t.
3.
Sketch the following surfaces and identify them by name (label the axes!):
(a) 2x2 + z 2 − y = 1
(b) x2 + 3y 2 = 5
(c) 2x2 + z 2 − y 2 = −1.
4.
Calculate the arc length of the curve r(t) = hcos t, sin t, ti from the point (1, 0, 0) to the
point of the intersection with the line x = −1, y = −1 + s, z = πs.
5.
(Bonus question +10%) Find an equation for the surface consisting of all points P for
which the distance from P to the x-axis is twice the distance from P to yz-plane. Identify
the surface.