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Chapter 3: Q. 20 (page 78)

For the three vectors shown in FIGURE EX3.20, A鈫�+B鈫�+C鈫�=1j^.What is vector B鈫�?

a. Write B鈫�in component form.

b. Write B鈫�as a magnitude and a direction.

Short Answer

Expert verified

(a) B鈫�=-3i^+5j^.

(a) The magnitude ofB鈫�is37and the direction is59.03鈭�.

Step by step solution

01

Part (a) Step 1. Given information

The given figure is,

andA鈫�+B鈫�+C鈫�=1j^.We need to determine the vectorB鈫�in component form.

02

Step 2. Calculation

From the figure,

A鈫�=3i^,C鈫�=-4j^.

A鈫�+B鈫�+C鈫�=1j^.

3i^+B鈫�-4j^=1j^.

B鈫�=-3i^+5j^.

03

Part (b) Step 1. Given information

The given figure is,

andA鈫�+B鈫�+C鈫�=1j^.We need to writeB鈫�as a magnitude and direction.

04

Step 2. Calculation

From part (a), B鈫�=-3i^+5j^.

role="math" B鈫�=-32+52.

=9+25.

=34.

tan胃=ByBx.

tan胃=5-3.

胃=tan-15-3.

=59.03鈭�.

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Most popular questions from this chapter

I A runner is training for an upcoming marathon by running around a 100-m-diameter circular track at constant speed. Let a coordinate system have its origin at the center of the circle with the -axis pointing east and the -axis north. The runner starts at and runs \(2.5\) times around the track in a clockwise direction. What is his displacement vector? Give your answer as a magnitude and direction.

FIGURE P3.26shows vectors A鈫�&B鈫�. Find D鈫�=2A鈫�+B鈫�. Write your answer in component form.

Kami is walking through the airport with her two-wheeled suitcase. The suitcase handle is tilted 40掳 from vertical, and Kami pulls parallel to the handle with a force of 120 N. (Force is measured in newtons, abbreviated N.) What are the horizontal and vertical components of her applied force?

Let A鈫�=4i^鈭�2j^, B鈫�=鈭�3i^+5j^and C=A+B.

a. Write vector C鈫�in component form.

b. Draw a coordinate system and on it show vectorsA鈫�,B鈫�, andC鈫�.

c. What are the magnitude and direction of vector C鈫�?

What are the x- and y-components of the velocity vector shown in FIGURE EX3.19?
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