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

1. spndsh

|dw:1355251229553:dw|

2. spndsh

do i distribute the 1/2 or the (a+b)?

3. hartnn

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

also [na mb pc] = mnp [a b c ]

5. hartnn

*and

6. spndsh

so i wouldn't simplify the inside of the brackets?

7. hartnn

[cX 2a.b] = 2 [a b c]

8. hartnn

i think i mis-interpreted the question....

9. hartnn

|dw:1355252100635:dw|

10. hartnn

=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

if you could understand.... ask if there is any doubt in any step.

12. spndsh

just one question whats the operation inside the bracket i.e [b c a]?

13. hartnn

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

if any 2 or more vectors are same, then box product =0 [a a b] = [b b a] = ... = 0

15. hartnn

or u meant to ask [a b c] = a.bXc ?

16. spndsh

yes

17. spndsh

thanks so much!

18. hartnn

hmm...welcome ^_^