State whether TRUE or FALSE:
The equation of a line, which is parallel to `2 hati + hatj + 3 hatk` and which passes through the point `(5,-2,4)` is `(x-5)/(2) =(y+2)/(-1) = (z-4)/(3).`

Answer

To determine whether the statement is TRUE or FALSE, we need to analyze the given line equation and check if it meets the criteria of being parallel to the specified direction vector and passing through the given point.

### Step-by-Step Solution:

1. **Identify the Direction Ratios of the Given Line:**
The direction ratios of the line given in the question are derived from the vector `2i + j + 3k`. Thus, the direction ratios are:
- \( a = 2 \)
- \( b = 1 \)
- \( c = 3 \)

2. **Identify the Point Through Which the Line Passes:**
The line is said to pass through the point \( (5, -2, 4) \). We denote this point as:
- \( (x_1, y_1, z_1) = (5, -2, 4) \)

3. **Write the General Equation of the Line:**
The general form of the equation of a line in three-dimensional space that passes through a point \( (x_1, y_1, z_1) \) and has direction ratios \( (a, b, c) \) is given by:
\[ \frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c} \]
Substituting the values we have:
\[ \frac{x - 5}{2} = \frac{y + 2}{1} = \frac{z - 4}{3} \]

4. **Compare with the Given Equation:**
The equation provided in the question is:
\[ \frac{x - 5}{2} = \frac{y + 2}{-1} = \frac{z - 4}{3} \]
Here, we notice that the direction ratio for \( y \) is given as \(-1\) instead of \(1\).

5. **Conclusion:**
Since the direction ratio for \( y \) in the provided equation does not match the direction ratio derived from the line to which it is supposed to be parallel, the statement is FALSE.

### Final Answer:
**FALSE**