`(vec A*vec B)+|vec A+vec B|^(2)=`

Shiw tgat |vec A= vec B|^2 - |vec A- vec B|^2 =4 vec A. vec B .

If vec A and vec B are two non-zero vectors such that |vec A+vec B|=(|vec A-vec B|)/(2) and |vec A|=2|vec B| then the angle between vec A and vec B is theta such that cos theta=-(m)/(n) (where m and n are positive integers and (m)/(n) lowest form then find m+n

Prove that (vec a+vec b)*(vec a+vec b)=|vec a|^(2)+|vec b|^(2) and only if vec a,vec b are perpendicular,given vec a!=vec 0,vec b!=vec 0

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec vdot vec a=0a n d vec vdot vec b=1a n d[ vec v vec a vec b]=1 is vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^) d. none of these

For any two non zero vectors write the value of (|vec a+vec b|^(2)+|vec a-vec b|^(2))/(|vec a|^(2)+|vec b|^(2))

If vec a=mvec b+vec c. The scalar m is (vec c*vec b-vec a*vec c)/(a^(2)) (vec c*vec a-vec b*vec c)/(c^(2)) (vec a*vec b-vec b*vec c)/(b^(2)) (vec a-vec c)/(vec b)

If vec a is parallel to vec b xxvec c ,then (vec a xxvec b)*(vec a xxvec c) is equal to |vec a|^(2)(vec b*vec c) b.|vec b|^(2)(vec a*vec c) c.|vec c|^(2)(vec a*vec b) d.none of these

If (vec a-vec b) * (vec a + vec b) = 0, then (a) vec a and vec b are perpendicular (b) vec a and vec b are parallel (c) | vec a | = | vec b | (d) vec a = 2vec b

Let vec a , vec b , vec c are three vectors , such that vec a + vec b + vec c = vec 0 .If , |vec a|=3 , |vec b|=4 and | vec c|=5 , then the value of, |vec a+vec b|^(2) + |vec b-vec c|^(2) + |vec c+vec a|^(2) , equal to :

If vec a,vec b and vec c are unit vectors satisfying |vec a-vec b|^(2)+|vec b-vec c|^(2)+|vec c-vec a|^(2)=9 then |2vec a+5vec b+5vec c| is.