Question

which is a sketch of \\(\overrightarrow{mn}\\) and \\(\overrightarrow{nx}\\)?

Explanation:

To determine the correct sketch of \(\overrightarrow{MN}\) and \(\overrightarrow{NX}\), we analyze the direction and endpoints of the vectors:

Key Concepts:

• A vector \(\overrightarrow{AB}\) has an initial point \(A\) and a terminal point \(B\), with an arrow pointing from \(A\) to \(B\).
• For \(\overrightarrow{MN}\), the initial point is \(M\) and the terminal point is \(N\) (arrow from \(M\) to \(N\)).
• For \(\overrightarrow{NX}\), the initial point is \(N\) and the terminal point is \(X\) (arrow from \(N\) to \(X\)).

Analyzing the Options:

1. Top - Left Diagram: \(\overrightarrow{MN}\) (arrow from \(M\) to \(N\)) and \(\overrightarrow{PX}\) (not \(\overrightarrow{NX}\))—incorrect.
2. Top - Right Diagram: \(\overrightarrow{MN}\) (arrow from \(M\) to \(N\)) and \(\overrightarrow{NX}\) (arrow from \(N\) to \(X\))—matches the vector definitions.
3. Bottom - Left Diagram: Vectors are not \(\overrightarrow{MN}\) and \(\overrightarrow{NX}\) (direction/endpoints do not align)—incorrect.
4. Bottom - Right Diagram: Vectors are not \(\overrightarrow{MN}\) and \(\overrightarrow{NX}\) (direction/endpoints do not align)—incorrect.

Answer:

The top - right diagram (with \(M\) connected to \(N\) by \(\overrightarrow{MN}\) and \(N\) connected to \(X\) by \(\overrightarrow{NX}\)) is the correct sketch.