Given `vec(a)+vec(b)+vec(c )+vec(d)=vec(O)`, which of the following statements is/are correct.

Options

A. `vec(a),vec(b),vec(c )` and `vec(d)` must each be a zero vector
B. The magnitude of `(vec(a)+vec(c))` can equals the magnitude of `(vec(b)+vec(d))`.
C. The magnitude of `vec(a)` can never be greater than the sum of the magnitudes of `vec(b),vec(c )` and `vec(d)`.
D. `vec(b)+vec(c )` must lie in the plane of `vec(a)` and `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

Answer

B, C, D

Explanation

`{:(vec(a)+vec(b)+vec(c)+vec(d)=0,,),(vec(a)+vec(c)=-(vec(b)+vec(d)),,),(|vec(a)+vec(c)|=|vec(b)+vec(d)|,,"B is correct"),(|vec(a)|=|vec(b)+vec(c)+vec(d)|,,"C is correct"):}`
Resultant of three non collinear vector is zero only when they are co-planar and if `vec(a)` and `vec(d)` are collinear then `vec(b)+vec(c )` must be in line of `vec(a)` and `vec(d)`