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spndsh Group Title

Simplify: Using Vector Algebra: 1/2 (a +b) dot [c cross (2a +b)]

  • 2 years ago
  • 2 years ago

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  1. spndsh Group Title
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    |dw:1355251229553:dw|

    • 2 years ago
  2. spndsh Group Title
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    do i distribute the 1/2 or the (a+b)?

    • 2 years ago
  3. hartnn Group Title
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    if i remember properly, cX(a.b) is the scalar triple product or box product denoted by [a b c] ans a. [a b c] = b. [a b c] = c. [a b c] = 0 so if u distribute (a+b), you'll get final answer as 0

    • 2 years ago
  4. hartnn Group Title
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    also [na mb pc] = mnp [a b c ]

    • 2 years ago
  5. hartnn Group Title
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    *and

    • 2 years ago
  6. spndsh Group Title
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    so i wouldn't simplify the inside of the brackets?

    • 2 years ago
  7. hartnn Group Title
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    [cX 2a.b] = 2 [a b c]

    • 2 years ago
  8. hartnn Group Title
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    i think i mis-interpreted the question....

    • 2 years ago
  9. hartnn Group Title
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    |dw:1355252100635:dw|

    • 2 years ago
  10. hartnn Group Title
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    =0 + 1/2 [a c b]+ 1/2 b . 2c X a + 1/2 b . c X b =0 + 1/2 [a c b]+1/2 [b c a]+ 1/2[b c b] =0 -1/2 [a b c] +1/2 [a b c] + 0 =0+0+0=0 now this seems right.

    • 2 years ago
  11. hartnn Group Title
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    if you could understand.... ask if there is any doubt in any step.

    • 2 years ago
  12. spndsh Group Title
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    just one question whats the operation inside the bracket i.e [b c a]?

    • 2 years ago
  13. hartnn Group Title
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    cyclic change doesn't change sign [a b c] = [b c a] = [c a b] else, sign changes [a b c] = -[a c b ] = -[b a c]

    • 2 years ago
  14. hartnn Group Title
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    if any 2 or more vectors are same, then box product =0 [a a b] = [b b a] = ... = 0

    • 2 years ago
  15. hartnn Group Title
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    or u meant to ask [a b c] = a.bXc ?

    • 2 years ago
  16. spndsh Group Title
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    yes

    • 2 years ago
  17. spndsh Group Title
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    thanks so much!

    • 2 years ago
  18. hartnn Group Title
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    hmm...welcome ^_^

    • 2 years ago
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