The vector r is equal to

• (r·i) + (r·j) + (r·k)
• (r·j) + (r·k) + (r·i)
• (r·k) + (r·i) + (r·j)
• (r·r)(i + j + k)

The equation you've provided seems to involve vector notation and operations. Let's break it down for clarity.

Understanding the Vector Components

The vector r can be expressed in terms of its components along the unit vectors i, j, and k, which represent the x, y, and z axes, respectively.

Breaking Down the Expression

• r·i: This represents the dot product of vector r with the unit vector i.
• r·j: Similarly, this is the dot product with the unit vector j.
• r·k: This is the dot product with the unit vector k.

Each of these dot products gives you a scalar value that indicates how much of vector r lies in the direction of each unit vector.

Combining the Components

The expression you provided seems to suggest a combination of these dot products. It can be interpreted as:

• (r·i) + (r·j) + (r·k): This sums the contributions of vector r in all three dimensions.
• (r·r)(i + j + k): This indicates a scaling of the vector sum by the magnitude of r squared.

Final Interpretation

In essence, the equation combines the projections of vector r onto the axes and scales them, which can be useful in various applications such as physics and engineering to analyze vector behavior in three-dimensional space.