Find the ratio in which the line segment joining the points (2,4,5) and (3,-5,4) is divide by the yz-plane.

Explanation

To find the ratio in which the line segment joining the points \( A(2, 4, 5) \) and \( B(3, -5, 4) \) is divided by the YZ-plane, we can follow these steps:

### Step 1: Understand the YZ-plane
The YZ-plane is defined by the equation \( x = 0 \). This means we need to find the point on the line segment \( AB \) where the x-coordinate is 0.

### Step 2: Use the section formula
Let the point of intersection of the line segment \( AB \) with the YZ-plane be \( P(0, y, z) \). We can express the coordinates of point \( P \) using the section formula. If \( P \) divides \( AB \) in the ratio \( m:n \), then the coordinates of \( P \) can be given as:

...