Question

The direction ratios of the line joining the points \( (2, 3, 4) \) and \( (-1, 4, -3) \) is:

• A. \( \pm (3, -1, 7) \)
• B. \( \pm (-3, -1, 7) \)
• C. \( \pm (3, 1, 7) \)
• D. \( \pm (3, -1, -7) \)
• E. \( \pm (-3, 1, 7) \)

Hint:

To find direction ratios, subtract the coordinates of the first point from the coordinates of the second point.

Answer 1

The Correct Option is A

Step 1: The direction ratios of a line joining two points \( P(x_1, y_1, z_1) \) and \( Q(x_2, y_2, z_2) \) are given by: \[ l = x_2 - x_1, \quad m = y_2 - y_1, \quad n = z_2 - z_1. \] Step 2: For the given points \( P(2, 3, 4) \) and \( Q(-1, 4, -3) \): \[ l = -1 - 2 = -3, \quad m = 4 - 3 = 1, \quad n = -3 - 4 = -7. \] Thus, the direction ratios are \( (-3, 1, -7) \), and the required direction ratios are \( \pm(3, -1, 7) \).