Given ` vec A + vec B+ vec C + vec D =0`, which of the following statements are correct ?
(a) ` vec A, vec B ,vec C ` abd ` vec D` each must be a null vector.
(b) The magnitude of ` ( vec A + vec C)` equals the magnitude of ` ( vec B + vec D)`.
(c) The magnitude of ` vec A` can never be greater than the sum of the magnitude of ` vec B , vec C ` and `vec D`.
(d) ` vec B + vec C` must lie in the plane of ` vec A + vec D`. if `vec A` and `vec D` are not collinear and in the line of ` vec A` and `vec D`, if they are collinear.

Explanation

a) This statement is not correct. Each need not not be a null vector. Even when `veca=-vecb` and `vecc = -vecd`, they can form a null vector.
b) This statement is correct. When `|veca+vecc|=|vecb+vecd|`, the addition may be a null vector, if `veca+vecc=-(vecb+vecd)` and are collinear.
c) This statements is correct. Let `|veca|gt|vecb+vecc+vecd|`. If it is true the vector sum cannot be zero. Even if `vecb, vecc, vecd` from a triangle, the vector sum `vecb+vecc=vecd=0` but then `veca+vecb+vecc+vecd` is not zero.
d) This statement is correct. If `vecb+vecc` do not lie in the plane of `veca+vecd`, the vector sum `(veca+vecb)+(vecc+vecd)` is not zero because the addends will have different magnitude nad different direction.