Let `vec r xx veca = vec b xx veca` and `vecc vec.r=0`, where `veca.vecc ne 0`, then `veca.vecc(vecr xx vecb)+(vecb.vecc)(veca xx vecr)` is equal to __________.

Answer

To solve the problem, we need to analyze the given expressions step by step.

### Given:
1. \( \vec{r} \times \vec{a} = \vec{b} \times \vec{a} \)
2. \( \vec{c} \cdot \vec{r} = 0 \)
3. \( \vec{a} \cdot \vec{c} \neq 0 \)

We need to find the value of:
\[ \vec{a} \cdot \vec{c} (\vec{r} \times \vec{b}) + (\vec{b} \cdot \vec{c})(\vec{a} \times \vec{r}) \]

### Step 1: Analyze the first condition
From the first condition, we have:
\[ \vec{r} \times \vec{a} = \vec{b} \times \vec{a} \]

This implies that the vectors \( \vec{r} \) and \( \vec{b} \) are related through the vector \( \vec{a} \).

### Step 2: Cross product with vector \( \vec{c} \)
Now, we take the cross product of both sides with \( \vec{c} \):
\[ \vec{c} \times (\vec{r} \times \vec{a}) = \vec{c} \times (\vec{b} \times \vec{a}) \]

Using the vector triple product identity, \( \vec{x} \times (\vec{y} \times \vec{z}) = (\vec{x} \cdot \vec{z})\vec{y} - (\vec{x} \cdot \vec{y})\vec{z} \), we can expand both sides:
- Left-hand side:
\[ \vec{c} \times (\vec{r} \times \vec{a}) = (\vec{c} \cdot \vec{a}) \vec{r} - (\vec{c} \cdot \vec{r}) \vec{a} \]
- Right-hand side:
\[ \vec{c} \times (\vec{b} \times \vec{a}) = (\vec{c} \cdot \vec{a}) \vec{b} - (\vec{c} \cdot \vec{b}) \vec{a} \]

### Step 3: Set the two sides equal
Equating both sides gives us:
\[ (\vec{c} \cdot \vec{a}) \vec{r} - (\vec{c} \cdot \vec{r}) \vec{a} = (\vec{c} \cdot \vec{a}) \vec{b} - (\vec{c} \cdot \vec{b}) \vec{a} \]

### Step 4: Substitute \( \vec{c} \cdot \vec{r} = 0 \)
Since \( \vec{c} \cdot \vec{r} = 0 \), the equation simplifies to:
\[ (\vec{c} \cdot \vec{a}) \vec{r} = (\vec{c} \cdot \vec{a}) \vec{b} \]

### Step 5: Factor out \( \vec{c} \cdot \vec{a} \)
If \( \vec{c} \cdot \vec{a} \neq 0 \), we can divide both sides by \( \vec{c} \cdot \vec{a} \):
\[ \vec{r} = \vec{b} \]

### Step 6: Substitute back into the expression
Now substituting \( \vec{r} = \vec{b} \) into the expression we need to evaluate:
\[ \vec{a} \cdot \vec{c} (\vec{b} \times \vec{b}) + (\vec{b} \cdot \vec{c})(\vec{a} \times \vec{b}) \]

### Step 7: Simplify the expression
Since \( \vec{b} \times \vec{b} = \vec{0} \), the first term becomes:
\[ \vec{a} \cdot \vec{c} \cdot \vec{0} = \vec{0} \]

Thus, we are left with:
\[ (\vec{b} \cdot \vec{c})(\vec{a} \times \vec{b}) \]

### Step 8: Analyze the second term
Now, since \( \vec{a} \times \vec{b} \) is perpendicular to both \( \vec{a} \) and \( \vec{b} \), and if \( \vec{b} \cdot \vec{c} \) is not zero, we can conclude that the entire expression evaluates to zero because the cross product of two parallel vectors is zero.

### Final Result
Thus, the final answer is:
\[ \boxed{0} \]