What is the condition for `vec A+vec B=vec A-vec B?`

What is the condition for magnitude of vec(A) + vec(B) to be equal to that of vec(A) -vec(B) ?

Three vectors vec a, vec b and vec c satisfy the condition vec a + vec b + vec b + vec c = vec 0 .Evaluate the quantity mu = vec a * vec b + vec b * vec c + vec c * vec a , if | vec a | = 1 | vec b | = 4 and | vec c | = 2

Three vectors vec a ,\ vec b ,\ vec c satisfy the condition vec a+ vec b+ vec c= vec0 . Evaluate the quantity mu= vec adot vec b+ vec bdot vec c+ vec cdot vec a ,\ if\ | vec a|=1,\ | vec b|=4\ a n d\ | vec c|=2.

Three vectors vec a , vec b , vec c satisfy the condition vec a+ vec b+ vec c= vec0 . Evaluate the quantity mu= vec adot vec b+ vec bdot vec c+ vec cdot vec a , if | vec a|=1, | vec b|=4 a n d | vec c|=2.

Three vectors veca, vec b and vec c satisfy the condition vec a + vec b + vec c = 0 .Evaluate the quantity. mu = vec a.vec b + vec b.vec c+ veca.vec c if |vec a| = 1, |vec b| = 4, |vec c| = 2

Suppose the three vectors vec a,vec b,vec c on a plane satisfy the condition that |vec a|=|vec b|=|vec c|=|vec a+vec b|=1;vec c is perpendicular to vec a and vec b*vec c<0, then

If vec a, vec b and vec c are unit vectors satisfying the condition vec a + vec b + vec c = 0 then show that vec a.vec b + vec a.vec c + vec b * vec c = - (3) / (2)

If vec a, vec b and vec c are unit vectors satisfying the condition vec a + vec b + vec c = 0 then shoe that vec a.vec b + vec a.vec c + vec b * vec c = - (3) / (2)

Under what condition will the equality : vec A xx vec B = vec A . vec B hold good ?

If vec a, vec b, vec c are unit vectors satisfying the condition veca+ vec b+ vec c= 0 then show that vec a. vec b+ vec b.vec c+ vec c. vec a= -3//2 .