Let A and B be two distinct points on the line L : 3 x − 6 = 2 y − 7 = − 2 z − 7 . Both A and B are at a distance 2 17 from the foot of perpendicular drawn from the point ( 1 , 2 , 3 ) on the

Question

Let A and B be two distinct points on the line L : 3 x − 6 ​ = 2 y − 7 ​ = − 2 z − 7 ​ . Both A and B are at a distance 2 17 ​ from the foot of perpendicular drawn from the point ( 1 , 2 , 3 ) on the line L . If O is the origin, then O A ⋅ OB is equal to:

TestHub · Accepted Answer

​ PQ ​ ⋅ b = 0 ⇒ 3 ( 3 λ + 5 ) + 2 ( 2 λ + 5 ) − 2 ( − 2 λ + 4 ) ⇒ 17 λ = − 17 ⇒ λ = − 1 Q ( 3 , 5 , 9 ) ​ Let A ( 3 μ + 6 , 2 μ + 7 , − 2 μ + 7 ) ( 3 μ + 3 ) 2 + ( 2 μ + 2 ) 2 + ( − 2 μ − 2 ) 2 = 68 ⇒ μ 2 + 2 μ − 3 = 0 μ = − 3 or μ = 1 A ( − 3 , 1 , 13 ) and B ( 9 , 9 , 5 ) OA ⋅ OB = − 27 + 9 + 65 = 47

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