The projection of a line segment on the co-ordinate 3, 4, 5, then its length is

Options

A. 12
B. 50
C. `5sqrt(2)`
D. none of these

Answer

To find the length of the projection of a line segment on the coordinates (3, 4, 5), we can follow these steps:

### Step 1: Understand the Concept of Projection
The projection of a line segment onto a coordinate axis is essentially the shadow that the line segment would cast on that axis. In this case, we are looking at the projection onto the vector defined by the coordinates (3, 4, 5).

### Step 2: Calculate the Length of the Vector
First, we need to find the length of the vector (3, 4, 5). The length (magnitude) of a vector \( \mathbf{v} = (x, y, z) \) is calculated using the formula:

\[ |\mathbf{v}| = \sqrt{x^2 + y^2 + z^2} \]

For our vector (3, 4, 5):

\[ |\mathbf{v}| = \sqrt{3^2 + 4^2 + 5^2} = \sqrt{9 + 16 + 25} = \sqrt{50} = 5\sqrt{2} \]

### Step 3: Conclusion
Thus, the length of the projection of the line segment on the coordinates (3, 4, 5) is \( 5\sqrt{2} \).

### Final Answer
The length of the projection of the line segment on the coordinates (3, 4, 5) is \( 5\sqrt{2} \).

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