If `hati,hatj` and `hatk` are unit vectors along X,Y `&` Z axis respectively, then what is the magnitude of `hati + hatj + hatk`

Explanation

To find the magnitude of the vector \( \hat{i} + \hat{j} + \hat{k} \), we can follow these steps:

### Step 1: Identify the vector components
The vector \( \hat{i} + \hat{j} + \hat{k} \) can be expressed in terms of its components:
- The component along the x-axis (i.e., \( \hat{i} \)) is 1.
- The component along the y-axis (i.e., \( \hat{j} \)) is 1.
- The component along the z-axis (i.e., \( \hat{k} \)) is 1.

So, we can represent the vector as:
\[ \mathbf{p} = 1 \hat{i} + 1 \hat{j} + 1 \hat{k} \]

### Step 2: Use the formula for the magnitude of a vector
The magnitude \( |\mathbf{p}| \) of a vector \( \mathbf{p} = a \hat{i} + b \hat{j} + c \hat{k} \) is given by the formula:
\[ |\mathbf{p}| = \sqrt{a^2 + b^2 + c^2} \]

### Step 3: Substitute the values into the formula
In our case, \( a = 1 \), \( b = 1 \), and \( c = 1 \). Thus, we substitute these values into the formula:
\[ |\mathbf{p}| = \sqrt{1^2 + 1^2 + 1^2} \]

### Step 4: Calculate the squares
Calculating the squares, we have:
\[ |\mathbf{p}| = \sqrt{1 + 1 + 1} = \sqrt{3} \]

### Step 5: Conclude the result
Thus, the magnitude of the vector \( \hat{i} + \hat{j} + \hat{k} \) is:
\[ |\mathbf{p}| = \sqrt{3} \]

### Final Answer
The magnitude of \( \hat{i} + \hat{j} + \hat{k} \) is \( \sqrt{3} \) units.

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