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

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Find the direction ratios of the line 2x = 3y = 5 - 4z ?
1. <2, 3, 5>
2. <6, 4, - 3>
3. <2, 3, - 4>
4. None of these

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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.