Question

The line joining the points \( (2,2,2) \) and \( (6,6,6) \) meets the line \[ \frac{x - 1}{3} = \frac{y - 2}{2} = \frac{z - 5}{-1} \] at the point

• A. \( (1,1,1) \)
• B. \( (2,2,2) \)
• C. \( (3,3,3) \)
• D. \( (4,4,4) \)
• E. \( (6,6,6) \)

Hint:

To find the intersection of two lines in 3D, express both in parametric form and solve for the parameters.

Answer 1

The Correct Option is D

To find the intersection point, we solve the parametric equations of the given lines. By equating the expressions, we find that the point of intersection is: \[ (4,4,4) \] Thus, the correct answer is (D).