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##### [solution] » MAT 273 Sections 11.1-11.3 Problem Set #3 11.1 1. Find the

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MAT 273 Sections 11.1-11.3 Problem Set #3 11.1 1. Find the**More:**

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MAT 273

MAT 273

Sections 11.1-11.3

Problem Set #3

11.1

1. Find the vector v with the given magnitude

v = 160

and the same direction as

2. Find the component form of vector v given its magnitude is

?

axis is =

v =5

u = ?12, 4

.

and the angle it makes with the positive x-

120° .

u =6

v =7

3. Find the component form of vector u + v given

and

and the angles that u and v make with

the positive x-axis are

? u = 0°

v

and ?=

45° .

4. Three forces with magnitudes 85 pounds, 110 pounds and 20 pounds act on an object at angles 70 , ?70 , and

100 , respectively, with the positive x-axis. Find the direction and magnitude of the resultant force.

(The choices below are given to two decimal places.)

MAT 273

Sections 11.1-11.3

Problem Set #3

5. Suppose a plane is flying in the direction 302° (relative to the west). Its speed with respect to the air is 600

kilometers per hour. The wind at the plane's altitude is from the southwest at 80 kilometers per hour (see figure).

What is its speed with respect to the ground? Round your answer to one decimal place.

6. Given u =

?1,5 and

=

v

3, ?2 ,

find v + u and

v ? u . Illustrate each operation on a coordinate grid.

11.2

7. Complete the square to write the following equation in the standard form for a sphere.

x 2 + y 2 + z 2 ? 8 x + 4 y ? 6 z + 25 =

0

8. Find a unit vector u in the direction opposite of

v = 8, 7, ?4

27

=

u

9. Find the vector v with the magnitude 2 and direction of

.

10, ?10,5

.

MAT 273

Sections 11.1-11.3

Problem Set #3

10. Given the vector v lies in the yz-plane, has magnitude 10, and makes an angle of 150° with the positive y-axis.

Find the component form of v.

11. Suppose the guy wire to a 100-foot tower has a tension of 550 pounds. Using the distances shown in the

figure, write the component form of the vector F representing the tension in the wire. Round numerical values in

your answer to the nearest integer.

11.3

12. Given

u = ?5, 7 ,

find

u ? u . Give an illustration of the operation.

=

v i ? 6 j + 7k , find ( u ? v ) v .

13. Given u= 4i + j ? 3k and

MAT 273

Sections 11.1-11.3

Problem Set #3

14. Find the angle between the vectors for u and v given below.

=

u

=

2, 4 , v

5,5

15. Determine whether u and v are orthogonal, parallel, or neither.

u=

5i + 5 j,

v=

?25i ? 25 j

16. Find the direction cosines of the vector u given below.

u = 1, ?1, ?3

u = 9,13

v = 1, 2 ,

and

find the projection of u onto v and the vector component of u orthogonal

17. Given

to v. Give an illustration of your results on the coordinate grid.

18. Suppose a car is towed using a force of 1200 newtons. The chain used to pull the car makes a 25° angle with

the horizontal. Find the work done in towing the car 4 kilometers using projections. Round your answer to two

decimal places.

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