Can the resultant be zero in case of :
(a) two unequal vectros
(b) three coplanar vectors
(c) three non- complanar vectors

Answer

(a) no ,(b) yes, (c) no

Explanation

(a) No,
Let two vectors be `vecA` and `vecB` and they are in opposite direction, then
`|vecA + vecB|=sqrt(A^(2) + B^(2) + 2AB cos 180^(@))`
`= sqrt(A^(2) + B^(2) - 2AB)`
`= sqrt((A - B)^(2))= A- B`
And, A- B is only zero if A = B.
(b) Yes
If magnitude of sum of two vectors is equal to magnitude of
third vectors and direction of resultant of sum of two vectors
is opposite to third one.
(c) No, because `cos 90^(@) = 0`.