1.If `vec a` and `vec b` are perpendicular,then `vec a times(vec a times(vec a times(vec a timesvec b)))` is equal to

Prove that (vec B timesvec c)*[vec A times(vec B timesvec C)]=0

Let veca,vecb and vecc be three vectors such that |veca |=sqrt(3),|vec b|=5 , vec b .vec c = 10 and the angle between vec b and vec c is pi/3, if vec a is perpendicular to the vector vec b xx vec c, then | veca xx (vecbxxvecc)| is equal to __________.

If vec a ,\ vec b ,\ vec c are any time mutually perpendicular vectors of equal magnitude a , then | vec a+ vec b+ vec c| is equal to a b. sqrt(2)a c. sqrt(3)a d. 2a e. none of these

If vec a , vec b and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( 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 and vec b are unit vectors such that ( vec a+ vec b).[(2 vec a+3 vec b)xx(3 vec a-2 vec b)]=0 , then angle between veca and vec b is a. 0 b. pi//2 c. pi d. indeterminate

If veca is any vector, then (vec a xx vec i)^2+(vec a xx vecj)^2+(veca xx vec k)^2 is equal to

If vec a and vec b are unequal unit vectors such that ( vec a- vec b)xx[( vec b+ vec a)xx(2 vec a+ vec b)]= vec a+ vec b , then angle theta between vec aa n d vec b is 0 b. pi//2 c. pi//4 d. pi

If vec a ,\ vec b ,\ 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 [ vec a\ vec b\ vec c] b. "\ "0"\ " c. 2[ vec a\ vec b\ vec c] d. -[ vec a\ vec b\ vec c]

Let vec a , vec b , and vec c are vectors such that | vec a|=3,| vec b|=4 and | vec c|=5, and ( vec a+ vec b) is perpendicular to vec c ,( vec b+ vec c) is perpendicular to vec a and ( vec c+ vec a) is perpendicular to vec bdot Then find the value of | vec a+ vec b+ vec c| .

If 4 vec a+5 vec b+9 vec c=0, then ( vec axx vec b)xx[( vec bxx vec c)xx( vec cxx vec a)] is equal to a vector perpendicular to the plane of a ,b ,c b. a scalar quantity c. vec0 d. none of these