Find the direction ratios of the line 2x = 3y = 5 - 4z ?

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

We will first be converting the above expression in standard form for comparison, i.e. we need to get rid of coefficients of x, y, and z, i.e. 2, 3, and 4 respectively.

LCM of 2, 3, and 4 is 12.

∴ 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.