If `vec axx vec b= vec cxxvec d` and `vec axxvec c= vec bxxvec d, vec a ne vec d, vec b ne vec c` then show that `vec b- vec c` is parallel to `vec a-vec d`

If vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , then show that vec a- vec d , is parallel to vec b- 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 .

If vec (a) xx vec(b) = vec (c ) xx vec(d) and vec (a) xx vec ( c) = vec (b) xx vec (d ) , show that vec(a) - vec (d) is parallel vec(b) - vec (c) , where to vec (a) != vec (d) and vec ( b) != vec (c )

Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec c and vec a is not a zero vector. Show that vec b= vec c dot

If 2vec a+ 3vecb + vec c = vec 0 , then show that vec axxvec b+vec bxxvec c+vec cxxvec a= 3(vec bxxvec c) .

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c . Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] ; then vec d equally inclined to vec a , vec b and vec c . (a) statement 1 is true but statement 2 is false. (b) statement 2 is true but statement 1 is false. (c)both the statements are true. (d) both the statements are false.

If | vec a|+| vec b|=| vec c| and vec a+ vec b= vec c , then find the angle between vec a and vec bdot

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). (vec b- vec c)!=0,

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). (vec b- vec c)!=0,

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