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Chapter 3: Q. 20 (page 78)

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

a. Write B→in component form.

b. Write B→as a magnitude and a direction.

Short Answer

Expert verified

(a) B→=-3i^+5j^.

(a) The magnitude ofB→is37and the direction is59.03∘.

Step by step solution

01

Part (a) Step 1. Given information

The given figure is,

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

02

Step 2. Calculation

From the figure,

A→=3i^,C→=-4j^.

A→+B→+C→=1j^.

3i^+B→-4j^=1j^.

B→=-3i^+5j^.

03

Part (b) Step 1. Given information

The given figure is,

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

04

Step 2. Calculation

From part (a), B→=-3i^+5j^.

role="math" B→=-32+52.

=9+25.

=34.

tanθ=ByBx.

tanθ=5-3.

θ=tan-15-3.

=59.03∘.

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