Mathematics · JEE | THREE DIMENSIONAL GEOMETRY

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The line passing through the points \( (1, -1, 2) \) and \( (3, 4, -2) \) is perpendicular to the line passing through \( (0, 3, 2) \) and \( (3, 5, 6) \). Reason (R): Two lines with direction ratios \( a_1, b_1, c_1 \) and \( a_2, b_2, c_2 \) are perpendicular if and only if \( \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} \). In the light of the above statements, choose the correct answer from the options given below:

1. A
   Both (A) and (R) are true and (R) is the correct explanation of (A).
2. B
   Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
3. C
   (A) is true but (R) is false.
4. D
   (A) is false but (R) is true.