Advanced Precalculus Chapter 8 Review Sheet

Advanced Precalculus Chapter 8 Review Sheet 1. Find a unit vector in the direction of

v

  7

i

 12

j

2. Find the direction of vector v if

v

  7

i

 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

v

  9

i

 2

j

and

w

 7

i

 5

j

11) Determine whether each pair of vectors are parallel, orthogonal of oblique: a)

v

 2

i

 2

j w



i



j v

 b) 3

i

4

i

  2 3

j j

c)

v

 3

i

 4

j w

 6

i

 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 P 1 and P 2 (1, 2, -3).

( 3, -1, 2)

16) Find the position vector for the vector having initial point P 1 ( 3, -1, 2) and terminal point P 2 (1, 2, -3).

17. Find the cross product:

v

  5

i

 6

j

 4

k w

  3

i

 4

j

 4

k

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

 3

i

 2

j



k w



i



j