Find the distance between each of pair of point:
`(0,3,0) and (6,0,2)`

Answer

To find the distance between the points \( A(0, 3, 0) \) and \( B(6, 0, 2) \), we will use the distance formula for points in three-dimensional space. The distance \( d \) between two points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) is given by:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]

### Step 1: Identify the coordinates of the points
Let:
- Point \( A \) be \( (x_1, y_1, z_1) = (0, 3, 0) \)
- Point \( B \) be \( (x_2, y_2, z_2) = (6, 0, 2) \)

### Step 2: Substitute the coordinates into the distance formula
Now, substitute the coordinates into the distance formula:

\[ d = \sqrt{(6 - 0)^2 + (0 - 3)^2 + (2 - 0)^2} \]

### Step 3: Calculate each term inside the square root
Calculating each term:
- \( (6 - 0)^2 = 6^2 = 36 \)
- \( (0 - 3)^2 = (-3)^2 = 9 \)
- \( (2 - 0)^2 = 2^2 = 4 \)

### Step 4: Add the squared terms
Now, add these values together:

\[ d = \sqrt{36 + 9 + 4} \]

Calculating the sum:

\[ 36 + 9 = 45 \]
\[ 45 + 4 = 49 \]

### Step 5: Take the square root
Now, take the square root of the sum:

\[ d = \sqrt{49} = 7 \]

### Conclusion
The distance between the points \( A(0, 3, 0) \) and \( B(6, 0, 2) \) is \( 7 \) units.

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