Correct Answer - Option 2 : <6, 4, - 3>

**CONCEPT****:**

The equation of a line with direction ratio <a, b, c> that passes through the point (x1, y1, z1) is given by the formula: \(\rm \frac{{x - {x_1}}}{a} = \frac{{y - {y_1}}}{b} = \frac{{z - {z_1}}}{c}\)

**CALCULATION****:**

Given: Equation of line is 2x = 3y = 5 - 4z

Dividing the above equation by 12 we get

\(⇒ \frac{{2x}}{{12}} = \frac{{3y}}{{12}} = \frac{{5\ -\ 4z}}{{12}}\;\)

\(⇒ \frac{x}{6} = \frac{y}{4} = \frac{{z - \frac{5}{4}}}{{ - 3}}\;\)

By comparing the above equation with \(\rm \frac{{x - {x_1}}}{a} = \frac{{y - {y_1}}}{b} = \frac{{z - {z_1}}}{c}\) we get

⇒ a = 6, b = 4 and c = -3

So, the direction ratios of the given line is: <6, 4, - 3>

Hence, the correct option is 2.