If ` vec ba n d vec c` are two-noncollinear vectors such that ` vec a||( vec bxx vec c),` then prove that `( vec axx vec b) . ( vec axx vec c) ` is equal to `| vec a|^2( vec bdot vec c)dot`

If vec a , vec ba n d vec c are non coplanar vectors and vec axx vec c is perpendicular to vec axx( vec bxx vec c), then the value of [axx( vec bxx vec c)]xx vec c is equal to a. [ vec a vec b vec c] b. 2[ vec a vec b vec c] vec b c. vec0 d. [ vec a vec b vec c] vec a

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

Let vec a , vec b ,a n d vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a]=[ vec a vec b vec c]^2dot

If vec a ,a n d vec b be two non-collinear unit vector such that vec axx( vec axx vec b)=1/2 vec b , then find the angle between vec a ,a n d vec bdot

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)

If vec a and vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b].

If vec a , vec ba n d vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c)dot[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c =0 , find the value of vec a.vec b+ vec b .vec c + vec c. vec a .

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec ca n d vec a is not a zero vector. Show that vec b= vec cdot