If a vector \(\vec{v} = 5\vec{i} - 3\vec{j} + \vec{k}\), what is the result of the operation \(7\vec{v}\)?

Step 1 ：First, we write down the vector \(\vec{v} = 5\vec{i} - 3\vec{j} + \vec{k}\).

Step 2 ：Then, we multiply the scalar value 7 to the vector \(\vec{v}\). This means multiplying the scalar value with each component of the vector separately. So, \(7\vec{v} = 7(5\vec{i} - 3\vec{j} + \vec{k})\)

Step 3 ：Finally, after the multiplication operation, we get \(7\vec{v} = 35\vec{i} - 21\vec{j} + 7\vec{k}\)