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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

Let B鈫�=5.0m,30鈭�counterclockwisefromvertical.Find the xandy-components of localid="1651138630094" B鈫�in each of the two coordinate systems shown in FIGURE EX3.18.

Let, A鈫�=4i^-2j^,B鈫�=-3i^+5j^andC鈫�=A鈫�+B鈫�.

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