The components of a vector `veca` along and perpendicular to a non-zero vector `vecb` are ________ and ___________, respectively.

Explanation

To find the components of a vector \(\vec{A}\) along and perpendicular to a non-zero vector \(\vec{B}\), we can follow these steps:

### Step 1: Find the component of \(\vec{A}\) along \(\vec{B}\)

The component of vector \(\vec{A}\) along vector \(\vec{B}\) is given by the formula:

\[ \text{Component of } \vec{A} \text{ along } \vec{B} = \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|^2} \vec{B} \]

Where:
- \(\vec{A} \cdot \vec{B}\) is the dot product of vectors \(\vec{A}\) and \(\vec{B}\).
- \(|\vec{B}|\) is the magnitude of vector \(\vec{B}\).

### Step 2: Find the component of \(\vec{A}\) perpendicular to \(\vec{B}\)

The component of vector \(\vec{A}\) perpendicular to vector \(\vec{B}\) is given by the formula:

\[ \text{Component of } \vec{A} \text{ perpendicular to } \vec{B} = \vec{A} - \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|^2} \vec{B} \]

### Final Answer

Thus, the components of vector \(\vec{A}\) along and perpendicular to vector \(\vec{B}\) are:

- **Along \(\vec{B}\)**: \(\frac{\vec{A} \cdot \vec{B}}{|\vec{B}|^2} \vec{B}\)
- **Perpendicular to \(\vec{B}\)**: \(\vec{A} - \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|^2} \vec{B}\)