1. Start with the given vector \( v = (5,7,-3) \).
2. Multiply each component of the vector \( v \) by \(-7\).
3. The result of the multiplication is:
-7 \cdot 5 = -35
-7 \cdot 7 = -49
-7 \cdot (-3) = 21
4. Thus, \(-7v = (-35, -49, 21)\).
5. Therefore, the answer is:
-7v = (-35, -49, 21)