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 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 ,\ vec b ,\ vec c are three unit vecrtors such that vec axx vec b= vec c ,\ vec bxx vec c= vec a ,\ vec cxx vec a= vec b Show that vec a ,\ vec b ,\ vec c form an orthonormal right handed triad of unit vectors.

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 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 bxx vec c!=0,w h e r e vec a , vec b ,a n d vec c are coplanar vectors, then for some scalar k prove that vec a+ vec c=k vec bdot

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 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

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.

Prove that [ vec a , vec b , vec c+ vec d]=[ vec a , vec b , vec c]+[ vec a , vec b , vec d]

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.