If ` vec axx vec b= vec cxx vec d\ a n d\ vec axx vec c= vec bxx vec d ,\ ` show that ` vec a- vec d` is parallel to ` vec b- vec c , w h e r e\ vec a!= vec d\ a n d\ vec b!= vec c`

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

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 to vec b- vec c , where vec a!= vec d and vec b!= vec c

If vec aX vec b= vec cX vec d and vec aX vec c= vec bx vec d , show that vec a- vec d is parallel to vec b- vec c , where vec a!= vec d and vec b!= vec cdot

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 axx vec b= vec axx vec c , vec a!= vec0a n d vec b!= vec c , show that vec b= vec c+t vec a for some scalar tdot

If vec axx vec b= vec bxx vec c!=0,\ then show that vec a+ vec c=m vec b ,\ w h e r e\ m is any scalar.

If vec axx vec b= vec bxx vec c!=0 , then show that vec a+ vec c=m vec b , where m is any scalar.

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 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 the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n (a) vec adot vec b+ vec bdot vec c+ vec c dot vec a=0 (b) vec axx vec b= vec bxx vec c= vec cxx vec a (c). vec adot vec b= vec bdot vec c= vec c dot vec a (d). vec axx vec b+ vec bxx vec c+ vec cxx vec a=0