If  and  are unit vectors along x, y and z axis respectively, then choose the wrong statement:

To analyze the question regarding unit vectors along the x, y, and z axes, let's consider what constitutes a unit vector in three-dimensional space.

1. Break Down the Problem

   • Identify the given unit vectors: Let's denote the unit vector along the x-axis as $\hat{i}$, along the y-axis as $\hat{j}$, and along the z-axis as $\hat{k}$.
   • Formulate what characteristics or properties are expected from unit vectors.

2. Relevant Concepts

   • A unit vector is defined as a vector with a magnitude of 1.
   • The dot product of any two different unit vectors (like $\hat{i} \cdot \hat{j}$, $\hat{j} \cdot \hat{k}$, or $\hat{k} \cdot \hat{i}$) is equal to 0, indicating they are orthogonal.
   • The magnitude of a unit vector is given as $|\hat{u}| = 1$ for any direction vector $\hat{u}$.

3. Analysis and Detail

   • We will analyze statements about unit vectors that could highlight which one is incorrect. Valid statements should include:
     1. $\hat{i} \cdot \hat{i} = 1$
     2. $\hat{j} \cdot \hat{j} = 1$
     3. $\hat{k} \cdot \hat{k} = 1$
     4. $\hat{i} \cdot \hat{j} = 0$, $\hat{j} \cdot \hat{k} = 0$, $\hat{k} \cdot \hat{i} = 0$

4. Verify and Summarize

   • Each valid statement should align with the properties of unit vectors. If any one statement contradicts these properties, it will be the wrong statement.

Final Answer

To choose the wrong statement, look for any statement that contradicts the defined properties of unit vectors. The wrong statement would likely be one that states the dot product of two different axes is non-zero or a unit vector has a magnitude that is not equal to 1. Without specific statements provided to choose from, I can't identify the exact incorrect statement. If you provide multiple statements regarding unit vectors, I can identify the erroneous one based on these principles.