spndsh
Simplify: Using Vector Algebra: 1/2 (a +b) dot [c cross (2a +b)]
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spndsh
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|dw:1355251229553:dw|
spndsh
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do i distribute the 1/2 or the (a+b)?
hartnn
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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
hartnn
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also [na mb pc] = mnp [a b c ]
hartnn
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*and
spndsh
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so i wouldn't simplify the inside of the brackets?
hartnn
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[cX 2a.b] = 2 [a b c]
hartnn
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i think i mis-interpreted the question....
hartnn
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|dw:1355252100635:dw|
hartnn
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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.
hartnn
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if you could understand....
ask if there is any doubt in any step.
spndsh
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just one question whats the operation inside the bracket i.e [b c a]?
hartnn
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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]
hartnn
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if any 2 or more vectors are same, then box product =0
[a a b] = [b b a] = ... = 0
hartnn
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or u meant to ask
[a b c] = a.bXc
?
spndsh
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yes
spndsh
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thanks so much!
hartnn
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hmm...welcome ^_^