A line l ⁡ passing through the origin is perpendicular to the lines l ⁡ 1 : 3 + t i ^ + - 1 + 2 t j ^ + 4 + 2 t k ^ , - ∞ < t < ∞ l ⁡ 2 : 3 + 2 s i ^ + 3 + 2 s j ^ + 2 + s k ^ , - ∞ < s < ∞ Then, the coordinate(s) of the point(s) on l ⁡ 2 at a distance of 1 7 from the point of intersection of l ⁡ and l ⁡ 1 is (are)

Step-by-step solution

Given l ⁡ 1 : 3 + t i ^ + - 1 + 2 t j ^ + 4 + 2 t k ^ , - ∞ t ∞ l ⁡ 2 : 3 + 2 s i ^ + 3 + 2 s j ^ + 2 + s k ^ , - ∞ s ∞ Direction ratios of line l 1 are 1 , 2 , 2 and line l 2 are 2 , 2 , 1 Let equation of line l is l : x - 0 a = y - 0 b = z - 0 c = k This line l is perpendicular to given line l 1 and l 2 . Hence a + 2 b + 2 c = 0 . . i l ⊥ l 1 2 a + 2 b + c = 0 . . i i l ⊥ l 2 Using equation i & i i a - 2 = b 3 = c - 2 Hence equation of l is x - 2 = y 3 = z - 2 = k 1 ↓ for l 1 , k 2 ↓ for l 2 Now A - 2 k 1 , 3 k 1