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 1.59P

Given r = 4 i 6 j + 2 k m (position vector) F = 20 i + 40 j 30 k N (force vector) λ = 0.8 j + 0.6 k (dimensionless unit vector) compute (a) r × F λ ; and (b) λ × r F .

Expert Solution
Check Mark
To determine

(a)

The scalar triple product r×F·λ.

Answer to Problem 1.59P

The scalar triple product r×F·λ is given by:

  r×F·λ=296N.m

Explanation of Solution

Given that:

Position vector, r=4i6j+2k m

Force Vector, F=20i+40j30k N

Dimensionless unit vector, λ=0.8j+0.6k

Concept Used: - We know that the scalar triple product A×B·C can be written in the following determinant form:

  A×B·C=| A x A y A z B x B y B z C x C y C z|

  A×B·C=| B y B z C y C z|Ax| B x B z C x C z|Ay+| B x B y C x C y|Az

Calculation: So the scalar triple product r×F·λ is calculated as given by:

  r×F·λ=|46220403000.80.6|

  r×F·λ=|40300.80.6|4|203000.6|(6)+|204000.8|2

  r×F·λ=(24+24)4+(12)6+(16)2

  r×F·λ=(48)4+(12)6+(16)2=296N.m

Expert Solution
Check Mark
To determine

(b)

The scalar triple product λ×r·F

Answer to Problem 1.59P

The scalar triple product λ×r·F is given by:

  λ×r·F=296N.m

Explanation of Solution

Given that:

Position vector, r=4i6j+2k m

Force Vector, F=20i+40j30k N

Dimensionless unit vector, λ=0.8j+0.6k

Concept Used: - We know that the scalar triple product A×B·C can be written in the following determinant form:

  A×B·C=| A x A y A z B x B y B z C x C y C z|

  A×B·C=| B y B z C y C z|Ax| B x B z C x C z|Ay+| B x B y C x C y|Az

Calculation: So the scalar triple product λ×r·F is calculated as given by:

  λ×r·F=|00.80.6462204030|

  λ×r·F=|624030|0|422030|(0.8)+|462040|0.6

  λ×r·F=(18080)0(12040)0.8+(160+120)0.6

  λ×r·F=(100)0(160)0.8+(280)0.6=296N.m

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Chapter 1 Solutions

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

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