vectors - adding two angle magnitude vectors contents: the basic concept step by step sample problem

Vectors - Adding two angle magnitude vectors

Contents:• The basic concept• Step by step• Sample problem

Vectors - AM + AM - Basics

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A:B:

Suppose you had to add these two vectors

Vectors - AM + AM - Basics

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A:

B:

Graphically you would place them tip to tail:

A + B

Vectors - AM + AM - Basics

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A:

B:

The components of the sum are the sum ofthe components.

A + B

Vectors - AM + AM - Step 1

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A:B:

Step 1: Break them into components

7

3

4

2

Vectors - AM + AM - Step 1

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A:B:

Step 1: A = 3 x + 7 yB = 4 x + 2 y

7

3

4

2

Vectors - AM + AM - Step 2

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A:B:

Step 2: A = 3 x + 7 yB = 4 x + 2 yA+B= 7 x + 9 y

7

3

4

2

Add like components

Vectors - AM + AM - Step 3

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Step 3: A = 3 x + 7 yB = 4 x + 2 yA+B= 7 x + 9 y

Find the newAM vector

A + B

7

9

tan-1(9/7) = 52o

(72 + 92) = 11

8.19 , 120.o W

Add these two angle magnitude vectors, and express their sum as an angle magnitude vector. Draw the resultant vector, and find its trig angle.

48.0o

7.00

A B

9.00

78.0o

1. AM to VC AM to VC2. VC + VC3. AM to VC

A = 4.684 x + 5.202 yB = -8.803 x + 1.871 yA + B = -4.119 x 7.073 y