If ` vec a= vec p+ vec q , vec pxx vec b=0a n d vec qdot vec b=0,` then prove that `( vec bxx( vec axx vec b))/( vec bdot vec b)= vec qdot`

Prove that (vec a-vec b)(vec b-vec c)xx(vec c-vec a)=0

If | vec a|=10 ,\ | vec b|=2\ a n d\ | vec axx vec b|=16 find vec adot vec bdot

Let vec a , vec b ,a n d vec c be vectors forming right-hand traid. Let 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 If xuuR^+, then x[ vec a vec b vec c]+([ vec p vec q vec r])/x b. x^4[ vec a vec b vec c]^2+([ vec p vec q vec r])/(x^2) has least value =(3/2)^(2//3) c. [ vec p vec q vec r]>0 d. none of these

The vectors vec a and vec b are not perpendicular and vec c and vec d are two vectors satisfying : vec b""xxvec c""= vec b"" xxvec d"",vec a * vec d=0 . Then the vector vec d is equal to : (1) vec b-(( vec bdot vec c)/( vec adot vec d)) vec c (2) vec c+(( vec adot vec c)/( vec adot vec b)) vec b (3) vec b+(( vec bdot vec c)/( vec adot vec b)) vec c (4) vec c-(( vec adot vec c)/( vec adot vec b)) vec b

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

Prove that if [ vec l vec m vec n] are three non-coplanar vectors, then [ vec l vec m vec n]( vec axx vec b)=| vec ldot vec a vec ldot vec b vec l vec mdot vec a vec mdot vec b vec m vec ndot vec a vec ndot vec b vec n| .

If vec a\ a n d\ vec b are unit vectors then write the value of | vec axx vec b|^2+( vec adot vec b)^2dot

The condition for equations vec rxx vec a= vec ba n d vec rxx vec c= vec d to be consistent is vec bdot vec c= vec adot vec d b. vec adot vec b= vec cdot vec d c. vec bdot vec c+ vec adot vec d=0 d. vec adot vec b+ vec cdot vec d=0

If vec a + vec b + vec c = 0, prove that (vec a xx vec b) = (vec b xx vec c) = (vec c xx vec a)

If vec a = vec b + vec c, vec b xxvec d = vec 0, vec c * vec d = 0 then (vec d xx (vec a xxvec d)) / (| vec d | ^ (2)) is always equal to