To prove: The formula ( u → × v → ) × w → = ( u → ⋅ w → ) v → − ( v → ⋅ w → ) u → and u → × ( v → × w → ) = ( u → ⋅ w → ) v → − ( u → ⋅ v → ) w → for the vectors u → = 2 i → , v → = 2 j → , w → = 2 k → by evaluating both the sides and comparing the results.

Question

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Answer 1

Question

Chapter 12, Problem 17AAE

(a)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→,v→=2j→,w→=2k→ by evaluating both the sides and comparing the results.

(b)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→−j→+k→,v→=2i→+j→−2k→,w→=−i→+2j→−k→ by evaluating both the sides and comparing the results.

(c)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→+j→,v→=2i→−j→+k→,w→=i→+2k→ by evaluating both the sides and comparing the results.

(d)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→+j→−2k→,v→=−i→−k→,w→=2i→+4j→−2k→ by evaluating both the sides and comparing the results.

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Answer 2

Question

Chapter 12, Problem 17AAE

(a)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→,v→=2j→,w→=2k→ by evaluating both the sides and comparing the results.

(b)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→−j→+k→,v→=2i→+j→−2k→,w→=−i→+2j→−k→ by evaluating both the sides and comparing the results.

(c)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→+j→,v→=2i→−j→+k→,w→=i→+2k→ by evaluating both the sides and comparing the results.

(d)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→+j→−2k→,v→=−i→−k→,w→=2i→+4j→−2k→ by evaluating both the sides and comparing the results.

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Answer 3

Question

Chapter 12, Problem 17AAE

(a)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→,v→=2j→,w→=2k→ by evaluating both the sides and comparing the results.

(b)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→−j→+k→,v→=2i→+j→−2k→,w→=−i→+2j→−k→ by evaluating both the sides and comparing the results.

(c)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→+j→,v→=2i→−j→+k→,w→=i→+2k→ by evaluating both the sides and comparing the results.

(d)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→+j→−2k→,v→=−i→−k→,w→=2i→+4j→−2k→ by evaluating both the sides and comparing the results.

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Answer 4

Question

Chapter 12, Problem 17AAE

(a)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→,v→=2j→,w→=2k→ by evaluating both the sides and comparing the results.

(b)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→−j→+k→,v→=2i→+j→−2k→,w→=−i→+2j→−k→ by evaluating both the sides and comparing the results.

(c)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→+j→,v→=2i→−j→+k→,w→=i→+2k→ by evaluating both the sides and comparing the results.

(d)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→+j→−2k→,v→=−i→−k→,w→=2i→+4j→−2k→ by evaluating both the sides and comparing the results.

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Answer 5

Chapter 12, Problem 17AAE

(a)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→,v→=2j→,w→=2k→ by evaluating both the sides and comparing the results.

(b)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→−j→+k→,v→=2i→+j→−2k→,w→=−i→+2j→−k→ by evaluating both the sides and comparing the results.

(c)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→+j→,v→=2i→−j→+k→,w→=i→+2k→ by evaluating both the sides and comparing the results.

(d)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→+j→−2k→,v→=−i→−k→,w→=2i→+4j→−2k→ by evaluating both the sides and comparing the results.

Answer 6

Chapter 12, Problem 17AAE

(a)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→,v→=2j→,w→=2k→ by evaluating both the sides and comparing the results.

Answer 7

Chapter 12, Problem 17AAE

(a)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→,v→=2j→,w→=2k→ by evaluating both the sides and comparing the results.

Answer 8

(b)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→−j→+k→,v→=2i→+j→−2k→,w→=−i→+2j→−k→ by evaluating both the sides and comparing the results.

Answer 9

(b)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→−j→+k→,v→=2i→+j→−2k→,w→=−i→+2j→−k→ by evaluating both the sides and comparing the results.

Answer 10

(c)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→+j→,v→=2i→−j→+k→,w→=i→+2k→ by evaluating both the sides and comparing the results.

Answer 11

(c)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→+j→,v→=2i→−j→+k→,w→=i→+2k→ by evaluating both the sides and comparing the results.

Answer 12

(d)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→+j→−2k→,v→=−i→−k→,w→=2i→+4j→−2k→ by evaluating both the sides and comparing the results.

Answer 13

(d)

To determine

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→+j→−2k→,v→=−i→−k→,w→=2i→+4j→−2k→ by evaluating both the sides and comparing the results.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→,v→=2j→,w→=2k→ by evaluating both the sides and comparing the results.

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→−j→+k→,v→=2i→+j→−2k→,w→=−i→+2j→−k→ by evaluating both the sides and comparing the results.

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=2i→+j→,v→=2i→−j→+k→,w→=i→+2k→ by evaluating both the sides and comparing the results.

To prove: The formula (u→×v→)×w→=(u→⋅w→)v→−(v→⋅w→)u→ and u→×(v→×w→)=(u→⋅w→)v→−(u→⋅v→)w→ for the vectors u→=i→+j→−2k→,v→=−i→−k→,w→=2i→+4j→−2k→ by evaluating both the sides and comparing the results.

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Chapter 12 Solutions