Compute the cross product C = A × B for each of the cases given in Prob. 1.51 Identify the units of each product.

Question

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Answer 1

Textbook Question

Chapter 1, Problem 1.58P

Compute the cross product C = A × B for each of the cases given in Prob. 1.51 Identify the units of each product.

Expert Solution

To determine

(a)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=52i−32j−48m2

Explanation of Solution

Given that:

A→=12j+8k ft

B→=4i−2j+3k ft

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|ijk01284−23|

A→×B→=|128−23|i−|0843|j+|0124−2|k

A→×B→=52i−32j−48m2

Expert Solution

To determine

(b)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=36i−60j−21Nm

Explanation of Solution

Given that:

A→=5i+3j N

B→=7i+12k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|30012|i−|50712|j+|5370|k

A→×B→=36i−60j−21Nm

Expert Solution

To determine

(c)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=−14i+30j+18Nm

Explanation of Solution

Given that:-

A→=3i+2j−k m

B→=−6i+2j−8k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|2−12−8|i−|3−1−6−8|j+|32−62|k

A→×B→=−14i+30j+18Nm

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Answer 2

Textbook Question

Chapter 1, Problem 1.58P

Compute the cross product C = A × B for each of the cases given in Prob. 1.51 Identify the units of each product.

Expert Solution

To determine

(a)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=52i−32j−48m2

Explanation of Solution

Given that:

A→=12j+8k ft

B→=4i−2j+3k ft

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|ijk01284−23|

A→×B→=|128−23|i−|0843|j+|0124−2|k

A→×B→=52i−32j−48m2

Expert Solution

To determine

(b)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=36i−60j−21Nm

Explanation of Solution

Given that:

A→=5i+3j N

B→=7i+12k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|30012|i−|50712|j+|5370|k

A→×B→=36i−60j−21Nm

Expert Solution

To determine

(c)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=−14i+30j+18Nm

Explanation of Solution

Given that:-

A→=3i+2j−k m

B→=−6i+2j−8k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|2−12−8|i−|3−1−6−8|j+|32−62|k

A→×B→=−14i+30j+18Nm

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Answer 3

Textbook Question

Chapter 1, Problem 1.58P

Compute the cross product C = A × B for each of the cases given in Prob. 1.51 Identify the units of each product.

Expert Solution

To determine

(a)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=52i−32j−48m2

Explanation of Solution

Given that:

A→=12j+8k ft

B→=4i−2j+3k ft

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|ijk01284−23|

A→×B→=|128−23|i−|0843|j+|0124−2|k

A→×B→=52i−32j−48m2

Expert Solution

To determine

(b)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=36i−60j−21Nm

Explanation of Solution

Given that:

A→=5i+3j N

B→=7i+12k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|30012|i−|50712|j+|5370|k

A→×B→=36i−60j−21Nm

Expert Solution

To determine

(c)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=−14i+30j+18Nm

Explanation of Solution

Given that:-

A→=3i+2j−k m

B→=−6i+2j−8k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|2−12−8|i−|3−1−6−8|j+|32−62|k

A→×B→=−14i+30j+18Nm

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Answer 4

Textbook Question

Chapter 1, Problem 1.58P

Compute the cross product C = A × B for each of the cases given in Prob. 1.51 Identify the units of each product.

Expert Solution

To determine

(a)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=52i−32j−48m2

Explanation of Solution

Given that:

A→=12j+8k ft

B→=4i−2j+3k ft

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|ijk01284−23|

A→×B→=|128−23|i−|0843|j+|0124−2|k

A→×B→=52i−32j−48m2

Expert Solution

To determine

(b)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=36i−60j−21Nm

Explanation of Solution

Given that:

A→=5i+3j N

B→=7i+12k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|30012|i−|50712|j+|5370|k

A→×B→=36i−60j−21Nm

Expert Solution

To determine

(c)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=−14i+30j+18Nm

Explanation of Solution

Given that:-

A→=3i+2j−k m

B→=−6i+2j−8k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|2−12−8|i−|3−1−6−8|j+|32−62|k

A→×B→=−14i+30j+18Nm

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution

To determine

(a)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=52i−32j−48m2

Explanation of Solution

Given that:

A→=12j+8k ft

B→=4i−2j+3k ft

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|ijk01284−23|

A→×B→=|128−23|i−|0843|j+|0124−2|k

A→×B→=52i−32j−48m2

Expert Solution

To determine

(b)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=36i−60j−21Nm

Explanation of Solution

Given that:

A→=5i+3j N

B→=7i+12k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|30012|i−|50712|j+|5370|k

A→×B→=36i−60j−21Nm

Expert Solution

To determine

(c)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=−14i+30j+18Nm

Explanation of Solution

Given that:-

A→=3i+2j−k m

B→=−6i+2j−8k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|2−12−8|i−|3−1−6−8|j+|32−62|k

A→×B→=−14i+30j+18Nm

Answer 8

Expert Solution

To determine

(a)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=52i−32j−48m2

Explanation of Solution

Given that:

A→=12j+8k ft

B→=4i−2j+3k ft

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|ijk01284−23|

A→×B→=|128−23|i−|0843|j+|0124−2|k

A→×B→=52i−32j−48m2

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

(a)

The cross product C = A→×B→

Answer 13

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=52i−32j−48m2

Answer 14

Explanation of Solution

Given that:

A→=12j+8k ft

B→=4i−2j+3k ft

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|ijk01284−23|

A→×B→=|128−23|i−|0843|j+|0124−2|k

A→×B→=52i−32j−48m2

Answer 15

Expert Solution

To determine

(b)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=36i−60j−21Nm

Explanation of Solution

Given that:

A→=5i+3j N

B→=7i+12k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|30012|i−|50712|j+|5370|k

A→×B→=36i−60j−21Nm

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

(b)

The cross product C = A→×B→

Answer 20

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=36i−60j−21Nm

Answer 21

Explanation of Solution

Given that:

A→=5i+3j N

B→=7i+12k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|30012|i−|50712|j+|5370|k

A→×B→=36i−60j−21Nm

Answer 22

Expert Solution

To determine

(c)

The cross product C = A→×B→

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=−14i+30j+18Nm

Explanation of Solution

Given that:-

A→=3i+2j−k m

B→=−6i+2j−8k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|2−12−8|i−|3−1−6−8|j+|32−62|k

A→×B→=−14i+30j+18Nm

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

(c)

The cross product C = A→×B→

Answer 27

Answer to Problem 1.58P

The cross product C = A→×B→ is given by:

A→×B→=−14i+30j+18Nm

Answer 28

Explanation of Solution

Given that:-

A→=3i+2j−k m

B→=−6i+2j−8k m

Concept: -We know that the cross product C = A→×B→ is given by:

A→×B→=|ijk a 1 a 2 a 3 b 1 b 2 b 3|

A→×B→=| a 2 a 3 b 2 b 3|i−| a 1 a 3 b 1 b 3|j+| a 1 a 2 b 1 b 2|k

Calculation: -

The cross product C = A→×B→ is given by:

A→×B→=|2−12−8|i−|3−1−6−8|j+|32−62|k

A→×B→=−14i+30j+18Nm

Answer 29

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Compute the cross product C = A × B for each of the cases given in Prob. 1.51 Identify the units of each product.

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Answer to Problem 1.58P

Explanation of Solution

Answer to Problem 1.58P

Explanation of Solution

Answer to Problem 1.58P

Explanation of Solution

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Chapter 1 Solutions