1. Sec 7.4 – Vector Matrices and Transforms Name:

1. Determine the rectangular form

of the 3 dimensional vector 퐴퐵⃗. Given that the points A and B are defined as 퐴: (2,−3,−4) and 퐵: (4, 5, 5) as shown in the graph.

2. Find the rectangular form of the vector from point A to point B.

a. A( −3, 2, 5) B(6, −2, 2) b. A( 1, −3, 0) B(8, −3, 1) c. A( 4, −2, 7) B(4, 4, −6)

3. Sketch a graph of the 3 dimensional vector shown below in standard position:

푣⃗: ⟨−2, 4, 2⟩

M. Winking © Unit 7-4 pg. 135

A

B

4. Describe the vector CD

in standard position at the right using component vectors , ,i j k

.

5. Find the magnitude of the vector in standard position.

6. Describe the vector GH

in standard position at the right using component vectors , ,i j k

.

7. Find the magnitude of the vector in standard position.

8. Using algebra find the resultant vector of CD GH

from problems #4 and #6.

9. Given the vectors 2,1,5v

and 3, 2, 4w

find the following:

a. 2 3v w

b. 3v w

c. 2 4v w

2

-2

5

2

-2

y

x

z

CD

2

-2

-5 2

-2

y

x

z

GH

M. Winking © Unit 7-4 pg. 136

10. Determine the spherical form of the 3 dimensional vector 푣⃗: ⟨−2, 2,4⟩

11. Determine the spherical form of the 3 dimensional vector 푢⃗: ⟨−4,−3, 2⟩

M. Winking © Unit 7-4 pg. 137

12. A satellite is located in space is orbiting space about

250 miles above Maine. The monitoring station in Houston, Texas can tell the satellite is 1450 miles due East, 1280 miles due North, and 250 miles above the Earth. If we simplify the problem and consider all measures given to be linear (i.e. assuming the curvature of the Earth wasn’t used to determine the distances), what is the distance in miles from the monitoring station to the satellite? Can you determine the azimuthal angle (i.e. horizontal angle) using degrees East of North using the monitoring station as the origin? Can you determine the angle of elevation the satellite dish should be set to in order to aim at the satellite?

13. A blimp air ship is ascending vertically at 3 miles per hour due to its buoyancy. The ship is also being propelled by a propeller at 25 miles per hour due East and a wind is blowing due South at a rate of 5 miles per hour. How fast is the air ship actually moving? Can you determine the azimuthal angle heading (i.e. horizontal angle) using degrees East of North using the blimp as the origin?

3 m

ph

25 mph E

S

UP

M. Winking © Unit 7-4 pg. 137