Math 265
Professor Lieberman
September 13, 2010
PRACTICE FIRST IN-CLASS EXAM
DIRECTIONS: This practice is only intended to show the level of difficulty for Friday’s
exam. The topics on the actual exam may be different from those represented here.
1. Find the sum u + v, the difference u − v, the magnitudes kuk and kvk, the dot
product u · v, and the cross-product u × v for the vectors
u = h1, 0, 1i,
v = h2, 3, 5i.
2. Find the velocity v, the acceleration a, and the speed s for the position vector
1
r(t) = i + (6t5 − 5)6 j + tk
t
at time t = 1.
3. Find the parametric equations of the tangent line to the curve x = 2t2 , y = 4t, z = t3
at t = 1.
4. Find the acceleration a, the unit tangent vector N, and the curvature κ of the curve
t2
r(t) = i + 5 cos tj + 5 sin tk
8
at time t = π.