Let the point, on the line passing through the points P ( 1 , − 2 , 3 ) and Q ( 5 , − 4 , 7 ) , farther from the origin and at distance of 9 units from the point P , be ( α , β , γ ) . Then α 2 + β 2

Question

Let the point, on the line passing through the points P ( 1 , − 2 , 3 ) and Q ( 5 , − 4 , 7 ) , farther from the origin and at distance of 9 units from the point P , be ( α , β , γ ) . Then α 2 + β 2 + γ 2 is equal to :

TestHub · Accepted Answer

PQ line ​ 4 x − 1 ​ = − 2 y + 2 ​ = 4 z − 3 ​ pt ( 4 t + 1 , − 2 t − 2 , 4 t + 3 ) distance 2 = 16 t 2 + 4 t 2 + 16 t 2 = 81 t = ± 2 3 ​ pt ( 7 , − 5 , 9 ) α 2 + β 2 + γ 2 = 155 ​ option (1)

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Options:

Doubts & Discussion