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Chapter 3: Q. 15 (page 77)

Let A = 4i - 2j, B = -3i + 5j, and E = 2A + 3B.
a. Write vector E in component form.
b. Draw a coordinate system and on it show vectors A, B, and E .
c. What are the magnitude and direction of vector E?

Short Answer

Expert verified

a) The vector E is -i^+11j^

b) The vectors are drawn in the coordinate system

c) The magnitude of the vector E is 11.04

Step by step solution

01

Write the given information

A→=4i^-2j^,B→=-3i^+5j^E→=2A→+3B→

02

 Step 2: a) To determine vector E

The vector E is given by;
E→=2A→+3B→E→=2(4i^-2j^)+3(-3i^+5j^)E→=8i^-4j^-9i^+15j^E→=-i^+11j^
Thus, the vector E is-i^+11j^

03

b) To draw the vectors in the coordinate system 

The vectors A, B, and E are shown below in the coordinate system

04

c) To determine the magnitude of E

The vector E is given by -i^+11j^
The magnitude of the vector is given by

E→=12+112=1+121=122=11.04
Thus, the magnitude of the vector E is 11.04

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Most popular questions from this chapter

Are the following statements true or false? Explain your answer.

a. The magnitude of a vector can be different in different coordinate systems.

b. The direction of a vector can be different in different coordinate systems.

c. The components of a vector can be different in different coordinate systems.

II A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 6.0m/s. A wise elder duck finally realizes that the solution is to fly at an angle to the wind. If the ducks can fly at 8.0m/srelative to the air, what direction should they head in order to move directly south?

The position of a particle as a function of time is given by CALCr→=(5i^+4j^)t2m, where t is in seconds.

a. What is the particle's distance from the origin at localid="1651417420923" t=0,2, and localid="1651417427817" 5s
?

b. Find an expression for the particle's velocitylocalid="1651417455538" v→as a function of time.

c. What is the particle's speed at localid="1651417472266" t=0,2, and localid="1651417482255" 5s?

II Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction.

a.B=−4i^+4j^

b.r→=(−2.0i^−1.0j^)cm

c.v→=(−10i^−100j^)m/s

d.a=(20i^+10j^)m/s2

While vacationing in the mountains you do some hiking. In the morning, your displacement is S→morning=(2000m, east )+(3000m, north )+(200m, vertical \()\). After lunch, your displacement is S→afternoon=(1500m, west )+(2000m, north )−(300m, vertical).

a. At the end of the hike, how much higher or lower are you compared to your starting point?

b. What is the magnitude of your net displacement for the day?
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