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 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 are three vectors such that vec adot\ vec b= vec adot\ vec c and vec a\ x\ vec b= vec a\ x\ vec c ,\ vec a\ !=0 , then show that vec b= vec c .

If vec a ,\ vec b ,\ vec c are three vectors such that vec a. vec b= vec a.\ vec c and vec a\ xx\ vec b= vec a\ xx\ vec c ,\ vec a\ !=0 , then show that vec b= vec c .

If vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k , then find the vaue of | vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec a vec bdot vec a dot vec c dot vec a dot vec c dot vec a dot vec c dot vec a| .

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

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

The condition for equations vec rxx vec a= vec ba n d vec rxx vec c= vec d to be consistent is vec bdot vec c= vec adot vec d b. vec adot vec b= vec c dot vec d c. vec bdot vec c+ vec adot vec d=0 d. vec adot vec b+ vec c dot vec d=0

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.

Let vec a , vec b , vec c be unit vectors such that vec adot vec b= vec adot vec c=0 and the angle between vec ba n d vec c is pi/6,t h a t vec a=+-2( vec bxx vec c)dot