If ` vec a=2 vec i+3 vec j- vec k , vec b=- vec i+2 vec j-4 vec k a n d vec c= vec i+ vec j+ vec k ,` then find thevalue of `( vec axx vec b)dot(( vec axx vec c)dot)`

If | vec a|=2| vec b|=5 and | vec axx vec b|=8, then find the value of vec a . vec bdot

If vec a , vec b , vec c are unit vectors such that vec a. vec b=0= vec a. vec c and the angle between vec b and vec c is pi/3, then find the value of | vec axx vec b- vec axx vec c| .

If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx vec c = vec cxxvec a .

Let the pairs a , b,and c ,d each determine a plane. Then the planes are parallel if a. ( vec axx vec c)xx( vec bxx vec d)= vec0 b. ( vec axx vec c).( vec bxx vec d)= vec0 c. ( vec axx vec b)xx( vec cxx vec d)= vec0 d. ( vec axx vec b).( vec cxx vec d)= vec0

Let vec a= vec i- vec k , vec b=x vec i+ vec j+(1-x) vec k and vec c=y vec i+x vec j+(1+x-y) vec k . Then [ vec a vec b vec c] depends on (A) only x (B) only y (C) Neither x nor y (D) both x and y

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

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

Let vec a and vec b be unit vectors such that | vec a+ vec b|=sqrt(3) . Then find the value of (2 vec a+5 vec b).((3 vec a+ vec b+ vec axx vec b))dot

If ( vec axx vec b)^2+( vec a.vec b)^2=144 and | vec a|=4, then find the value of | vec b|dot

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