Question

The symmetric equation of the straight line passing through the points \( (-1, 4, 2) \) and \( (-3, 0, 5) \) is

• A. \( \frac{x-1}{-2} = \frac{y+4}{-4} = \frac{z+2}{3} \)
• B. \( \frac{x+1}{2} = \frac{y-4}{4} = \frac{z-2}{5} \)
• C. \( \frac{x+1}{-2} = \frac{y-4}{-4} = \frac{z-2}{3} \)
• D. \( \frac{x-3}{-2} = \frac{y+1}{-4} = \frac{z+5}{3} \)
• E. \( \frac{x+1}{4} = \frac{y-4}{-4} = \frac{z-2}{3} \)

Hint:

The direction ratios of a line passing through two points \( A \) and \( B \) are obtained by subtracting the coordinates of \( A \) from \( B \).

Answer 1

The Correct Option is C

The symmetric equation of a straight line passing through two points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) is given by: \[ \frac{x - x_1}{x_2 - x_1} = \frac{y - y_1}{y_2 - y_1} = \frac{z - z_1}{z_2 - z_1} \] Substituting the given points, we obtain: \[ \frac{x+1}{-2} = \frac{y-4}{-4} = \frac{z-2}{3} \] Thus, the correct answer is (C).