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spndsh

  • 3 years ago

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

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  1. spndsh
    • 3 years ago
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    |dw:1355251229553:dw|

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

  3. hartnn
    • 3 years ago
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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

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

  5. hartnn
    • 3 years ago
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    *and

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

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

  8. hartnn
    • 3 years ago
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    i think i mis-interpreted the question....

  9. hartnn
    • 3 years ago
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    |dw:1355252100635:dw|

  10. hartnn
    • 3 years ago
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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.

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

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

  13. hartnn
    • 3 years ago
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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]

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

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

  16. spndsh
    • 3 years ago
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    yes

  17. spndsh
    • 3 years ago
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    thanks so much!

  18. hartnn
    • 3 years ago
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    hmm...welcome ^_^

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