A plane mirror is lying in x-y plane .Object velocity is
` V_0=(2 hati-3 hatj+4 hatk) m//s`. Find the image velocity.

Explanation

To find the image velocity of an object moving in front of a plane mirror, we can follow these steps:

### Step 1: Understand the given information
We have a plane mirror lying in the x-y plane, and the velocity of the object is given as:
\[ V_0 = 2 \hat{i} - 3 \hat{j} + 4 \hat{k} \, \text{m/s} \]

### Step 2: Recall the formula for image velocity
The image velocity \( V_i \) of an object in front of a plane mirror is given by the formula:
\[ V_i = -V_0 \]
This means that the image velocity is equal to the negative of the object velocity.

### Step 3: Substitute the object velocity into the formula
Now, we will substitute the given object velocity into the formula:
\[ V_i = - (2 \hat{i} - 3 \hat{j} + 4 \hat{k}) \]

### Step 4: Simplify the expression
Distributing the negative sign gives:
\[ V_i = -2 \hat{i} + 3 \hat{j} - 4 \hat{k} \]

### Step 5: Write the final answer
Thus, the image velocity is:
\[ V_i = -2 \hat{i} + 3 \hat{j} - 4 \hat{k} \, \text{m/s} \]

### Summary
The image velocity of the object is:
\[ V_i = -2 \hat{i} + 3 \hat{j} - 4 \hat{k} \, \text{m/s} \]

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