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`

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot

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

The condition for equations vec rxx vec a= vec ba n d vec rxx vec c= vec d to be consistent is a. 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 parallel to vec b- vec c

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 a , vec b , and vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c| .

Value of [ vec axx vec b , vec axx vec c , vec d] is always equal to a. ( vec adot vec d)[ vec a vec b vec c] b. ( vec adot vec c)[ vec a vec b vec d] c. ( vec adot vec b)[ vec a vec b vec d] d. none of these

If vec aa n d vec b are two vectors and angle between them is theta, then | vec axx vec b|^2+( vec adot vec b)^2=| vec a|^2| vec b|^2 | vec axx vec b|=( vec adot vec b),iftheta=pi//4 vec axx vec b=( vec adot vec b) hat n ,(w h e r e hat n is unit vector, ) if theta=pi//4 ( vec axx vec b)dot( vec a+ vec b)=0

Let vec aa n d vec b be two non-collinear unit vector. If vec u= vec a-( vec adot vec b) vec ba n d vec v= vec axx vec b ,t h e n| vec v| is a. | vec u| b. | vec u|+| vec udot vec a| c. | vec u|+| vec udot vec b| d. | vec u|+ hat udot| vec a+ vec b|

Given vec a=x hat i+y hat j+2 hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j ; vec a_|_ vec b , vec adot vec c=4. Then [ vec a vec b vec c]^2=| vec a| b. [ vec a vec b vec c]^=| vec a| c. [ vec a vec b vec c]^=0 d. [ vec a vec b vec c]^=| vec a|^2