If ` vec a=2 vec i+3 vec j- vec k , vec b=- vec i+2 vec j-4 vec ka 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 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].

Find lambda if the vectors vec a= vec i+3 vec j+ vec k , vec b= 2 vec i- vec j- vec k and vec c= lambda vec i+7 vec j+ 3 vec k are coplanar

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

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

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

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

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d)dot (vec b- vec c)!=0,

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

If vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k , then find the vaue of | vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec a vec bdot vec a vec cdot vec a vec cdot vec a vec cdot vec a| .

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