Name
MATH 107 PRACTICE
MIDTERM II 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. A.
(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 =
0_{
}
, then A, B and
C are collinear. B.
(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
x^{2} + z^{2}  e^{2y} = 0 _{
}
. This surface is formed by
revolving a generating curve about an axis. Find an equation of this generating curve and state the axis
of revolution. 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
x^{2} y^{2
} _{ } is
b^{2
} r^{2}
= _{ } given that
b^{2
} e^{2}
= 1 + 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
time progresses
