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The problem asks to find the equation of a line \( g \) that intersects two given lines, \( h \) and \( k \), and is also parallel to line \( j \).

Here’s a breakdown of the given information:

1. **Line \( h \)** is defined by the equation: 
   \[
   2x + y - 1 = 0
   \]
   
2. **Line \( k \)** is defined by the equation: 
   \[
   3x - y + z + 2 = 0
   \]

3. **Line \( j \)** has the parametric form: 
   \[
   \frac{x}{1} = \frac{y}{2} = \frac{z}{3}
   \]
   This suggests that the direction ratios of line \( j \) are proportional to \( 1:2:3 \).

### Steps to solve:

1. **Find direction ratios** of line \( j \) from its parametric form, which are \( (1, 2, 3) \).
   
2. **Determine the vector equation** of the required line \( g \), which must be parallel to line \( j \). Since line \( g \) is parallel to \( j \), the direction ratios of \( g \) should also be \( (1, 2, 3) \).

3. **Find intersection points** of line \( g \) with lines \( h \) and \( k \). To do this, express the parametric equations for line \( g \) using the direction ratios and plug them into the equations for \( h \) and \( k \). Solving this system will give the required points.

Would you like a more detailed step-by-step calculation for solving this system, or do you have a specific question regarding the approach?

### Additional questions:
1. How do you extract the parametric form of a line from a system of equations?
2. What is the geometric interpretation of two lines being parallel?
3. Can you explain how direction ratios help in defining the slope of a line in 3D?
4. How would you solve the system of equations for intersection points in 3D geometry?
5. Why do we equate the direction ratios when lines are parallel?

### Tip:
When dealing with lines in 3D, always try to first extract direction ratios to simplify your approach toward finding intersection points or determining parallelism.

Tentukan persamaan garis lurus g yang memotong kedua garis lurus h ≡ 2x + y − 1 = 0 dan k ≡ 3x − y + z + 2 = 0 = 4x + 5y − 2z − 3, serta sejajar garis lurus j ≡ x/1 = y/2 = z/3.

Learn how to find the equation of a line that intersects two given lines in 3D space and is parallel to another. This problem involves solving parametric equations and determining intersection points in three-dimensional geometry.

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