Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 10, Problem 29P

(a)

To determine

To find: A×B

(a)

Expert Solution
Check Mark

Answer to Problem 29P

  A×B=24 k^

Explanation of Solution

Given:

  A=4 i^B=6 i^+6 j^

Formula used:

The property of vector cross product:

  i^ ×j^=k^,  j^ ×k^=i^,  k^ ×i^=j^i^ ×i^=0,  j^ ×j^=0,  k^ ×k^=0

Calculation:

  A×B=4 i^×(6 i^+6 j^)=4×6(i^×i^)+4×6(i^×j^)=24×0+24 k^=24 k^

Conclusion:

  A×B=24 k^

(b)

To determine

To Find: A×B

(b)

Expert Solution
Check Mark

Answer to Problem 29P

  A×B=24 j^ 

Explanation of Solution

Given:

  A=4 i^B=6 i^+6 k^

Formula used:

The property of vector cross product:

  · i^ ×j^=k^,  j^ ×k^=i^,  k^ ×i^=j^· j^ ×i^=k^,  k^ ×j^=i^,  i^ ×k^=j^· i^ ×i^=0,  j^ ×j^=0,  k^ ×k^=0

Calculation:

  A×B=4 i^×(6 i^+6 k^)=4×6(i^×i^)+4×6(i^×k^)=24×0+24(j^)=24 j^ 

Conclusion:

  A×B=24 j^ 

(c)

To determine

To Find: A×B

(c)

Expert Solution
Check Mark

Answer to Problem 29P

  A×B=5k^

Explanation of Solution

Given:

  A=2 i^+3 j^B=3 i^+2 j^

Formula used:

The property of vector cross product:

  · i^ ×j^=k^,  j^ ×k^=i^,  k^ ×i^=j^· j^ ×i^=k^,  k^ ×j^=i^,  i^ ×k^=j^· i^ ×i^=0,  j^ ×j^=0,  k^ ×k^=0

Calculation:

  A×B=(2 i^+3 j^)×(3 i^+2 j^)=2×3(i^×i^)+2×2(i^×j^)+3×3(j^×i^)+3×2(j^×j^)=6×0+4k^+9(k^)+6×0=4k^9k^A×B=5k^

Conclusion:

  A×B=5k^

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