Given `vecA + vecB + vecC + vecD = vec0`, which of the following statements is not correct ?

Options

A. `vecA, vecB, vecC and vecD` must each be a null vector.
B. The magnitude of `(vecA + vecC)` equals the magnitude of `(vecB + vecD)`.
C. The magnitude of `vecA` can never be greater than the sum of the magnitudes of `vecB, vecC and vecD.`
D. `vecB + vecC` must lie in the plane of `vecA and vecD` if `vecA and vecD` are not collinear and in the line of `vecA and vecD`, if they are collinear.

Explanation

To solve the problem, we need to analyze the given equation and the statements provided in the options. The equation given is:

\[ \vec{A} + \vec{B} + \vec{C} + \vec{D} = \vec{0} \]

This means that the vector sum of \(\vec{A}\), \(\vec{B}\), \(\vec{C}\), and \(\vec{D}\) results in the zero vector. Let's evaluate each option to determine which statement is not correct.

### Step 1: Analyze Option 1
**Statement:** \(\vec{A}, \vec{B}, \vec{C}, \vec{D}\) must each be a null vector.

- This statement is incorrect because the vectors do not have to be null vectors. There are many combinations of vectors that can sum to zero without all being zero. For example, \(\vec{A} = \vec{B}\) and \(\vec{C} = -\vec{A}\) and \(\vec{D} = -\vec{B}\) would satisfy the equation without any of them being null vectors.

### Step 2: Analyze Option 2
**Statement:** \(|\vec{A} + \vec{C}| = |\vec{B} + \vec{D}|\).

- This statement is correct. From the equation \(\vec{A} + \vec{B} + \vec{C} + \vec{D} = \vec{0}\), we can rearrange it to \(\vec{A} + \vec{C} = -(\vec{B} + \vec{D})\). Taking the magnitude of both sides gives us \(|\vec{A} + \vec{C}| = |\vec{B} + \vec{D}|\).

### Step 3: Analyze Option 3
**Statement:** The magnitude of \(\vec{A}\) can never be greater than the sum of the magnitudes of \(\vec{B}\), \(\vec{C}\), and \(\vec{D}\).

- This statement is also correct. By the triangle inequality, the magnitude of one vector is always less than or equal to the sum of the magnitudes of the other vectors. Therefore, \(|\vec{A}| \leq |\vec{B}| + |\vec{C}| + |\vec{D}|\).

### Step 4: Analyze Option 4
**Statement:** The vector sum can be zero if \(\vec{B} + \vec{C}\) lies in the plane containing \(\vec{A}\) and \(\vec{D}\).

- This statement is correct. The vectors can indeed sum to zero if they are arranged in such a way that they form a closed triangle or if they are coplanar. The condition described in the statement is sufficient for the vector sum to be zero.

### Conclusion
After analyzing all options, we find that the first option is the only incorrect statement. Therefore, the answer is:

**The incorrect statement is Option 1.**