Name
Name Vector HW #1Component/polar/magnitude
1) A car is driving east-southeast (22.5[pic] south of east) at a speed of 55 miles per hour. Give the indicated representation of this velocity.
a) polar b) component
2) Give the component representation of a vector with length 1 and direction 218[pic] from the polar axis.
3) Give the component representation of the vector with initial point (-2, 1) and ending point (3, -5).
4) Find the length and direction of the plane vector represented by the arrow joining the point (3, 4) to (7, -1).
5) Find [pic]to the nearest tenth, when [pic]= (-6, 11).
6) Give the polar representation of vector (-16, 19).
7) Prove that the arrow joining (-1, 2) to (4, -1) represents the same vector as the arrow joining (3, -2) to (8, -5).
Name Vector HW #2 Sum/Difference
In 1 and 2 find [pic].
1) [pic] and [pic]
2) [pic] and [pic] (round to the nearest tenth)
3) Find the resultant force for the forces [pic] shown below.
4) If [pic], express [pic] in the indicated form.
a) polar b) component
5) Using [pic] find [pic].
Name Vector HW #3 Parallel Vectors and Equations
In 1 – 4 let [pic] and compute.
1) [pic] 2) [pic]
3) [pic] + [pic] 4) [pic]
5) Show that [pic] are parallel.
6) Show that the line passing through (-2, 2) and (0,8) is parallel to vector [pic].
7) Is the given vector parallel to [pic]?
a) [pic] b) [pic]
c) [pic]
8) Are [pic] parallel?
9) Write a vector equation for the following:
a) the line that passes through (-1, 4) that is parallel to the vector [pic]
b) the line that passes through (3, -2) that is parallel to the vector [pic]
10) Solve the quadratic equation by completing the square, express the roots in simplest radical form: [pic]
11) If a is even, and b is odd, then ab + a + b is which of the following?
a) always even
b) always odd
c) sometimes even, sometimes odd
12) Find [pic]f(x)
Name HW #4 Dot Product
In 1 – 4, let [pic] and compute.
1) [pic] 2) [pic]
3) [pic] 4) [pic]
In 5 – 8 find the measure of the angle between the two vectors.
5) (-3, -3) and (1, 2) 6) (4, 6) and (2, 7)
7) (-5, 0) and (0, -12) 8) [4, 94[pic]] and [19, 211[pic]]
9) Show that [pic]and [pic] are not orthogonal.
10) Find the center and radius of the circle with the following equation:
[pic]
Name HW #5 3 – D Coordinates
1) Use the grid to plot and label the following points:
A(0, -2, -3)
B(1, 3, -1)
C(4, 0, 2)
D (0, 3, 4)
2) In 3-space, the equation x = 0 describes which of the following?
(1) the x-axis (2) the y –axis (3) the xy-plane (4) the yz-plane
3) Use example 1 above in order to find the following:
a) the distance point C is from the origin.
b) the distance point A is from point B.
4) Find the center and radius of the sphere with the equation [pic].
Name HW #6 Vectors in 3 – Space
Examples: Let [pic]and find the following:
1) [pic] 2) [pic]
3) [pic] 4) [pic]
5) Find the angle between [pic].
6) Are [pic] orthogonal?
7) Find a vector that is orthogonal to [pic]
8) What value(s) of x make the following fraction undefined?
[pic]
9) Solve: [pic]
Name HW #7 Cross Product
1) Find [pic]for vectors [pic].
2) Verify that [pic] is perpendicular to both [pic].
3) a) Find z so that [pic].
b) Find a vector orthogonal to both [pic].
Name HW #8 Lines and Planes in 3 – Space
1) Let m be a line passing through the two points (8, 3, -5) and (-7, -3, 1). Describe m with
a) a vector equation.
b) the parametric equations.
2) Find an equation for the plane that is perpendicular to [pic]and contains the point (3, -5, 0).
3) Let M be the plane defined by the equation 6x – 4y +3z = 12. Show that (3, 0, -2) is a point on the plane.
4) Suppose [pic], [pic], and [pic].
Find the exact values of [pic] and [pic].
5) Is x – 2 a factor of [pic]? (Explain your answer)
-----------------------
-1
4
x
y
f(x)
7
z
-y
-x
[pic]
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