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 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 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 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 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 , where m is any scalar.

If vec(a)vec(b)vec(c ) and vec(d) are vectors such that vec(a) xx vec(b) = vec(c ) xx vec(d) and vec(a) xx vec(c ) = vec(b)xxvec(d) . Then show that the vectors vec(a) -vec(d) and vec(b) -vec(c ) are parallel.

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

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