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 a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

Let vec a , vec ba n d vec c be three non-coplanar vecrors and vec r be any arbitrary vector. Then ( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b) is always equal to [ vec a vec b vec c] vec r b. 2[ vec a vec b vec c] vec r c. 3[ vec a vec b vec c] vec r d. none of these

Prove that [ vec a, vec b, vec c + vec d] = [ vec a, vec b, vec c] + [ vec a, vec b , vec d] .

If vec axx( vec bxx vec c) is perpendicular to ( vec axx vec b)xx vec c , we may have a. ( vec a . vec c)| vec b|^2=( vec a . vec b)( vec b . vec c) b. vec adot vec b=0 c. vec adot vec c=0 d. vec bdot vec c=0

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 is parallel to vec bxx vec c , then ( vec axx vec b)dot( vec axx vec c) is equal to a. | vec a|^2( vec b . vec c) b. | vec b|^2( vec a . vec c) c. | vec c|^2( vec a . vec b) d. none of these

Let vec a , vec b , a n d vec c be three non-coplanar vectors and vec d be a non-zero vector, which is perpendicular to ( vec a+ vec b+ vec c)dot Now vec d=( vec axx vec b)sinx+( vec bxx vec c)cosy+2( vec cxx vec a)dotT h e n a. ( vec ddot( vec a+ vec b))/([ vec a vec b vec c])=2 b. ( vec ddot( vec a+ vec b))/([ vec a vec b vec c])=-2 c. minimum value of x^2+y^2 is pi^2//4 d. minimum value of x^2+y^2 is 5pi^2//4

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

Value of [ vec axx vec b vec axx vec c vec d] is always equal to ( vec a . vec d)[ vec a vec b vec c] b. ( vec a . vec c)[ vec a vec b vec d] c. ( vec a . vec b)[ vec a vec b vec d] d. none of these

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3