Suppose a, b, c are three vectors such that `abs(a)=7`. If a + b + c = 0, then `abs(a*b+a*c)=`_______

Answer

To solve the problem, we need to find the value of \( |a \cdot b + a \cdot c| \) given the conditions \( |a| = 7 \) and \( a + b + c = 0 \).

### Step-by-Step Solution:

1. **Understanding the Given Information:**
We know that:
- The magnitude of vector \( a \) is \( |a| = 7 \).
- The equation \( a + b + c = 0 \) implies that \( b + c = -a \).

2. **Taking the Dot Product:**
We can take the dot product of the equation \( a + b + c = 0 \) with vector \( a \):
\[ a \cdot (a + b + c) = a \cdot 0 \]
This simplifies to:
\[ a \cdot a + a \cdot b + a \cdot c = 0 \]

3. **Substituting the Magnitude of \( a \):**
We know that \( a \cdot a = |a|^2 = 7^2 = 49 \). Thus, we can rewrite the equation:
\[ 49 + a \cdot b + a \cdot c = 0 \]

4. **Solving for \( a \cdot b + a \cdot c \):**
Rearranging the equation gives us:
\[ a \cdot b + a \cdot c = -49 \]

5. **Finding the Magnitude:**
We need to find \( |a \cdot b + a \cdot c| \):
\[ |a \cdot b + a \cdot c| = |-49| = 49 \]

### Final Answer:
Thus, the value of \( |a \cdot b + a \cdot c| \) is \( \boxed{49} \).