First name:   Last name:

1.  Let \(\vec{v}\) be the vector in \(R^2\) of length 3 making a counterclockwise angle of \(20^o\) with the positive x-axis. Then in component form, \(\vec{v}\) is approximately

a.  \(\langle 2.82, 1.03\rangle\)

b.  \(\langle 2.72, 1.27\rangle\)

c.  \(\langle 2.60, 1.50\rangle\)

d.  \(\langle 2.46, 1.72\rangle\)

e.  \(\langle 2.12, 2.12\rangle\)

2.  Find \(c\) so that the points \( ( 1, 2)\), \( (c, 10)\), and \( (10, 14)\) are collinear.

a.  4

b.  5

c.  6

b.  7

c.  8

3.  Consider the points A(1,2,3), B(5,5,3), and C(3,4,4). Find the coordinates of D so that ABCD is a parallogram. Hint: this means that opposite sides must be parallel.

a.  (7, 7, 4)

b.  (3, 3, 2)

c.  (-1, 1, 4)

d.  (0, 0 ,0)

e.  (7, 8, 3)

4.  Find the center and the radius of the sphere \(x^2 + y^2 + z^2 = 2x + 4y + 6z + 2\).

a.  Center (1, 2, 3), radius 3.

b.  Center (-1, -2, -3), radius 3.

c.  Center (1, 2, 3), radius 4.

d.  Center (-1, -2, -3), radius 4.

e.  Center (0, 0, 0), radius 2x + 4y + 6z + 3.

In questions 5, 6, and 7 consider the triangle with vertices A(1,2,3), B(5,5,3), and C(3,4,4).

5.  Find cos\(\theta\) where \(\theta\) is the smallest angle in the triangle.

a.  -14/15

b.  -1/15

c.  0

d.  1/15

e.  14/15

6.  Classify this triangle as one of the following.

a.  Acute

b.  Right

c.  Obtuse

7.  Find the coordinates of D so that ABCD is a parallogram. Hint: this means that opposite sides must be parallel.

a.  (7, 7, 4)

b.  (3, 3, 2)

c.  (-1, 1, 4)

d.  (0, 0 ,0)

e.  (7, 8, 3)

8.  For how many different values of t would the vectors 〈t, t, -1〉,〈t, 1, 6〉 be orthogonal?

a.  None

b.  One

c.  Two

d.  Three

e.  Infinitely many