International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN: 9781305501607
Author: Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
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Textbook Question
Chapter 1, Problem 1.57P

Compute the dot product A - B for each of the following cases. Identify the units of each product.

A = 12 j + 8 k ft B = 4 i 2 j + 3 k ft A = 5 i + 3 j m B = 7 i 12 k N A = 3 j + 2 j-k m B = 6 i + 2 j 8 k m

Expert Solution
Check Mark
To determine

(a)

The dot product A·B

Answer to Problem 1.57P

The dot product A·B is given by:

  A·B=(0)(4)+(12)(2)+(8)(3)=0ft2

Explanation of Solution

Given that:

  A=12j+8k ft

  B=4i2j+3k ft

Concept: - We know that the dot product A·B is given by:

  A·B=(Axi+Ayj+Azk)·(Bxi+Byj+Bzk)

  =AxBx+AyBy+AzBz

Calculation: -

The dot product A·B is given by:

  A·B=(12j+8k)·(4i2j+3k)

  A·B=(0)(4)+(12)(2)+(8)(3)=0ft2

Expert Solution
Check Mark
To determine

(b)

The dot product A·B

Answer to Problem 1.57P

The dot product A·B is given by:

  A·B=(5)(7)+(3)(0)+(0)(12)=35Nm

Explanation of Solution

Given that:

  A=5i+3j N

  B=7i+12k m

Concept: - We know that the dot product A·B is given by:

  A·B=(Axi+Ayj+Azk)·(Bxi+Byj+Bzk)

  =AxBx+AyBy+AzBz

Calculation: -

The dot product A·B is given by:

  A·B=(5i+3j)·(7i+12k)

  A·B=(5)(7)+(3)(0)+(0)(12)=35Nm

Expert Solution
Check Mark
To determine

(c)

The dot product A·B

Answer to Problem 1.57P

The dot product A·B is given by:

  A·B=(3)(6)+(2)(2)+(1)(8)=6m2

Explanation of Solution

Given that: -

  A=3i+2jk m

  B=6i+2j8k m

Concept: - We know that the dot product A·B is given by:

  A·B=(Axi+Ayj+Azk)·(Bxi+Byj+Bzk)

  =AxBx+AyBy+AzBz

Calculation: -

The dot product A·B is given by:

  A·B=(3i+2jk)·(6i+2j8k)

  A·B=(3)(6)+(2)(2)+(1)(8)=6m2

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Chapter 1 Solutions

International Edition---engineering Mechanics: Statics, 4th Edition

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