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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