NameVector HW #1Component/polar/magnitude
1)A car is driving east-southeast (22.5 south of east) at a speed of 55 miles per hour. Give the indicated representation of this velocity.
a) polarb) component
2) Give the component representation of a vector with length 1 and direction 218 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 to the nearest tenth, when = (-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).
NameVector HW #2 Sum/Difference
In 1 and 2 find .
1) and
2) and (round to the nearest tenth)
3) Find the resultant force for the forces shown below.
4)If , express in the indicated form.
a) polarb) component
5) Using find .
NameVector HW #3 Parallel Vectors and Equations
In 1 – 4 let and compute.
1)2)
3) + 4)
5) Show that are parallel.
6)Show that the line passing through (-2, 2) and (0,8) is parallel to vector .
7)Is the given vector parallel to ?
a)b)
c)
8)Are parallel?
9)Write a vector equation for the following:
a) the line that passes through (-1, 4) that is parallel to the vector
b) the line that passes through (3, -2) that is parallel to the vector
10)Solve the quadratic equation by completing the square, express the roots in simplest radical form:
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 f(x)
NameHW #4 Dot Product
In 1 – 4, let and compute.
1)2)
3)4)
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] and [19, 211]
9) Show that and are not orthogonal.
10)Find the center and radius of the circle with the following equation:
NameHW #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 .
NameHW #6 Vectors in 3 – Space
Examples:Let and find the following:
1)2)
3)4)
5) Find the angle between .
6) Are orthogonal?
7) Find a vector that is orthogonal to
8)What value(s) of x make the following fraction undefined?
9)Solve:
NameHW #7 Cross Product
1)Find for vectors .
2) Verify that is perpendicular to both .
3)a) Find z so that .
b) Find a vector orthogonal to both .
NameHW #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 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 , , and .
Find the exact values of and .
5)Is x – 2 a factor of ? (Explain your answer)
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