Question

Question #8f5e6

Answer 1

`(vec d xx (vec a xx vec d))/(|vec d|^2)`

bac-cab rule for triple vec product
`= (vec a(vec d * vec d) - vec d (vec d * vec a) )/(|vec d|^2)`

As `vec d * vec d = |vec d|^2`
`= vec a - (vec d (vec d * vec b + vec d * vec c) )/(|vec d|^2)`

As `vec c*vec d = vec 0 = vec d*vec c`

And as `vec b xx vec d = vec 0 = |vec b|| vec c| sin theta \ hat n implies theta = k pi, k in mathcal(Z)` so `vec b * vec d = pm |vec b||vec d|`

`= vec a pm (vec d (abs(vec d) abs( vec b)) )/(|vec d|^2)`

`= vec a pm (vec d abs( vec b) )/(|vec d|)`

`= vec a pm hat d abs( vec b)`

just doesn't feel right but that's where i get it to come out