The lines ` vec r= vec a+lambda( vec bxx vec c)a n d vec r= vec b+mu( vec cxx vec a)` will intersect if a. ` vec axx vec c= vec bxx vec c` b. ` vec adot vec c= vec bdot vec c` c. `bxx vec a= vec cxx vec a` d. none of these

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then

If vec a+ vec b + vec c= 0 , show that vec axxvec b= vec bxx vec c= vec cxx vec a .

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 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 paralelto vec b- vec c

Let vec a , vec ba n d vec c be three non-coplanar vecrors and vec r be any arbitrary vector. Then ( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b) is always equal to [ vec a vec b vec c] vec r b. 2[ vec a vec b vec c] vec r c. 3[ vec a vec b vec c] vec r d. none of these

Let vec a , vec ba n d vec c be three non-coplanar vecrors and vec r be any arbitrary vector. Then ( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b) is always equal to [ vec a vec b vec c] vec r b. 2[ vec a vec b vec c] vec r c. 3[ vec a vec b vec c] vec r d. none of these

Let vec a , vec ba n d vec c be three non-coplanar vecrors and vec r be any arbitrary vector. Then ( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b) is always equal to [ vec a vec b vec c] vec r b. 2[ vec a vec b vec c] vec r c. 3[ vec a vec b vec c] vec r d. none of these

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 d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vector and |( vec d * vec c)( vec axx vec b)+( vec d* vec a)( vec bxx vec c)+( vec d*vec b)( vec cxx vec a)|=0, then a. | vec a|=| vec b|=| vec c| b. | vec a|+| vec b|+| vec c|=|d| c. vec a , vec b ,a n d vec c are coplanar d. none of these

If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vector and |( vec d * vec c)( vec axx vec b)+( vec d* vec a)( vec bxx vec c)+( vec d*vec b)( vec cxx vec a)|=0, then a. | vec a|=| vec b|=| vec c| b. | vec a|+| vec b|+| vec c|=|d| c. vec a , vec b ,a n d vec c are coplanar d. none of these