(i) Find the ratio in which yz-plane divides the join of points (2, 4, 7) and (-3,5,8).
(ii) Find the ratio in which yz-plane divides the line joining of the points (-3,1,4) and (2, -7, 3).

Explanation

To solve the problem, we will find the ratio in which the yz-plane divides the line segments joining the given points. The yz-plane is defined by the equation x = 0, so we will use the section formula to find the required ratios.

### Part (i): Find the ratio in which the yz-plane divides the join of points (2, 4, 7) and (-3, 5, 8).

1. **Identify the points**: Let A = (2, 4, 7) and B = (-3, 5, 8).

2. **Assume the division ratio**: Let the yz-plane divide the line segment AB in the ratio λ:1. The coordinates of the point of division, P, will be (0, y, z).

3. **Using the section formula**: The coordinates of point P can be expressed using the section formula:
\[ x = \frac{-3\lambda + 2 \cdot 1}{\lambda + 1} \]
Since P lies on the yz-plane, we set x = 0:
\[ 0 = \frac{-3\lambda + 2}{\lambda + 1} \]

4. **Solve for λ**:
\[ -3\lambda + 2 = 0 \implies 3\lambda = 2 \implies \lambda = \frac{2}{3} \]

5. **Express the ratio**: The ratio in which the yz-plane divides the line segment AB is λ:1, which is:
\[ \frac{2}{3}:1 = 2:3 \]

### Part (ii): Find the ratio in which the yz-plane divides the line joining the points (-3, 1, 4) and (2, -7, 3).

1. **Identify the points**: Let C = (-3, 1, 4) and D = (2, -7, 3).

2. **Assume the division ratio**: Let the yz-plane divide the line segment CD in the ratio k:1. The coordinates of the point of division, Q, will be (0, y, z).

3. **Using the section formula**: The coordinates of point Q can be expressed using the section formula:
\[ x = \frac{2k - 3}{k + 1} \]
Since Q lies on the yz-plane, we set x = 0:
\[ 0 = \frac{2k - 3}{k + 1} \]

4. **Solve for k**:
\[ 2k - 3 = 0 \implies 2k = 3 \implies k = \frac{3}{2} \]

5. **Express the ratio**: The ratio in which the yz-plane divides the line segment CD is k:1, which is:
\[ \frac{3}{2}:1 = 3:2 \]

### Final Answers:
- (i) The yz-plane divides the line segment joining points (2, 4, 7) and (-3, 5, 8) in the ratio 2:3.
- (ii) The yz-plane divides the line segment joining points (-3, 1, 4) and (2, -7, 3) in the ratio 3:2.