Advanced Precalculus
Chapter 8 Review Sheet
Advanced Precalculus Chapter 8 Review Sheet
1. Find a unit vector in the direction of v  7i  12 j
2. Find the direction of vector v if
v  7i  12 j
3. Given v of magnitude 20 and direction 210º
and w of magnitude 15 and direction 132º,
find v + w.
4. A vector v has initial point (-2, 3) and terminal point (7, 6). Find its position vector in component form.
5. An airliner’s navigator determines that the jet is flying
475 mph with a heading of N 41.5ºW, but the jet is
actually moving 415 mph in a direction N 52.3º W. What
is the velocity of the wind?
6. Multiply: [5(cos 30º + i sin 30 º)][7(cos 210 º + i sin 210 º)]
a) polar form of the answer:
b) standard form of the answer:
7) Divide:
a) polar form of the answer:
b) standard form of the answer:
8) Evaluate: (3 – 3i)6
a) polar form of the answer:
b) standard form of the answer:
9) Find the three cubed roots of -8
a) polar form:
b) standard form:
10) Find the angle θ between the vectors
and w  7i  5 j
v  9i  2 j
11) Determine whether each pair of vectors are parallel,
orthogonal of oblique:
a)
v  2i  2 j
wi j
v  3i  2 j
b) w  4i  3 j
v  3i  4 j
c) w  6i  8 j
12) Find the dot product v ∙ w if v = i and w = -3i + 4j
13) Find the work done by a force of 7 pounds acting in
the direction of 42 º to the horizontal in moving an
object 5 feet from (0, 0) and (5, 0).
14) An airplane has an air speed of 550 mph bearing
N30 ºW. The wind velocity if 50 mph in the direction
N30 ºE. Find the resultant vector (with exact
components) representing the path of the plane relative
to the ground. To the nearest tenth, what is the ground
speed of the plane? What is its direction?
15) Find the distance between the points P1 ( 3, -1, 2)
and P2 (1, 2, -3).
16) Find the position vector for the vector having initial
point P1 ( 3, -1, 2) and terminal point P2 (1, 2, -3).
17. Find the cross product:
v  5i  6 j  4k
w  3i  4 j  4k
18) Find the area of the parallelogram with one corner at
(-1, 0, 1) another at (2, 1, -2) and a third at (2, -1, 2).
19) Find a vector orthogonal to both v and w given:
v  3i  2 j  k
wi j