Find the equation of line which passes through a point (-1, 2, 3) and is parallel to a vector
having direction ratios (3, 4, 2).

Answer

To find the equation of the line that passes through the point (-1, 2, 3) and is parallel to the vector with direction ratios (3, 4, 2), we can follow these steps:

### Step 1: Identify the given point and direction ratios
We have:
- Point \( P(-1, 2, 3) \)
- Direction ratios \( (3, 4, 2) \)

### Step 2: Use the formula for the equation of a line in 3D
The equation of a line in 3D that passes through a point \( (x_1, y_1, z_1) \) and is parallel to a vector with direction ratios \( (a, b, c) \) is given by:
\[ \frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c} \]

### Step 3: Substitute the values into the formula
Substituting the point \( (-1, 2, 3) \) and the direction ratios \( (3, 4, 2) \):
- \( x_1 = -1 \)
- \( y_1 = 2 \)
- \( z_1 = 3 \)
- \( a = 3 \)
- \( b = 4 \)
- \( c = 2 \)

The equation becomes:
\[ \frac{x + 1}{3} = \frac{y - 2}{4} = \frac{z - 3}{2} \]

### Step 4: Write the final equation
Thus, the equation of the line is:
\[ \frac{x + 1}{3} = \frac{y - 2}{4} = \frac{z - 3}{2} \]