If ` vec ra n d vec s` are non-zero constant vectors and the scalar `b` is chosen such that `| vec r+b vec s|` is minimum, then the value of `|b vec s|^2+| vec r+b vec s|^2` is equal to a.`2| vec r|^2` b. `| vec r|^2//2` c. `3| vec r""|^2` d. `|r|^2`

vec a and vec b are two non-collinear vectors then the value of {(vec a)/(|vec a|^(2))-(vec b)/(|vec b|^(2))} is equal to

If vec a\ a n d\ vec b are unit vectors then write the value of | vec axx vec b|^2+( vec adot vec b)^2dot

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))

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 three non-zero vectors,prove that [vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

Let vec a xx vec b,vec b xx vec c,vec c xx vec a are non coplanar vectors and [[vec a,vec b,vec c]]=1.vec r is a vector such that vec r.vec a=vec r.vec b=vec r.vec c=2, then area of triangle whose vertices are vec a,vec b and vec c is (A) |vecr|/2 (2) 2|vecr| (C) |vecr|/4 (D) 4|vecr|

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0, then vec r is equal to

vec a,vec b,vec c are the three coplanar vectors and if vec r*vec a=vec r*vec b=vec r*vec c=0 then prove that vec r is a zero vector

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0 then vec r is equal to

vec a,vec b and vec c are three non-coplanar vectors and vec r is any arbitrary vector.Prove that [vec bvec cvec r]vec a+[vec c+vec avec r]vec b+[vec avec bvec r]vec c=[vec avec bvec c]vec r