(a) Incorrect statement

There are several other combinations that can result in the sum being zero(a + b + c + d = 0). It is not mandatory for all four vectors to be null vectors for the sum to be null vectors.

(b) Correct statement

a + b + c + d = 0

a + b = - (c + d)

Taking modulus on both sides yields magnitude

|a + b| = |-(c + d)|

|a + b| = |c + d|

Hence, the magnitude of (a + c) equals the magnitude of (b + d).

(c) Correct statement

a + b + c + d = 0

a = - (b + c + d)

Taking modulus on both sides yields magnitude

|a| = |-(b + c + d)|

|a| =|b + c + d|

The sum of the magnitudes of b, c, and d is equal to or less than the magnitude of a.

Hence, the magnitude of vector a will never exceed the sum of the magnitudes of vectors b, c, and d.

d) Correct statement

a + b + c + d = 0

a + (b + c) + d = 0

The sum of the three vectors a, (b+c) and d can only be nullified if (b+c) lies on a plane containing a and d,

If a and d are collinear, the vector (b + c) is in line with a and d, then the vector sum of all the vectors become zero.