Homework # 2 - Math 2250
The problems on this homework must be done alone. The honor code is in effect.
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 \(x^2 + y^2 + z^2 = 2x + 4y + 6z + 3\).
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.