MATH 107 PRACTICE
Please work out each of the given
problems. Credit will be based on
the steps that you show towards the final answer.
Show your work.
PROBLEM 1 Please answer
the following true or false. If
false, explain why or provide a counter example.
If true explain why.
(15 Points) If A,
B, and C are points, v
is the vector from A to B,
w is the vector from B
to C, and v x w =
, then A, B and
C are collinear.
(15 Points) If x
= x(t), y = y(t)
are parametric equations of a line then dx/dt
is a constant.
PROBLEM 2 (21 Points)
Consider the surface
x2 + z2 - e2y = 0
. This surface is formed by
revolving a generating curve about an axis. Find an equation of this generating curve and state the axis
PROBLEM 3 (21 Points)
Use vectors to find the equation of the line that passes through the point (2,3,4) and is perpendicular to the plane 5x - 4y + 2z = 7.
PROBLEM 4 (21 Points)
Find all points (if any) of horizontal and vertical tangency. Make sure to present your answer by listing the points not just the values of q.
x = cos q y = 2sin(2q)
PROBLEM 5 (21 Points)
Determine the area of the first quadrant loop of r = 3sin(2q)
PROBLEM 6 (21 Points)
Show that the polar equation for the hyperbola
PROBLEM 7 (21 Points)
Use vectors to determine if the triangle with vertices (1,0,1), (2,1,0), (0,0,4) is a right triangle.
PROBLEM 8 (21 Points)
Find parametric equations for
the a particle moves along the line through (1,4,2)
and (3,5,7) such that it is at the point (1,4,2)
when t = 0 is at the point
(3,5,7) when t = 2 and is speeding up as