Let P be the point ( 10 , − 2 , − 1 ) and Q be the foot of the perpendicular drawn from the point R ( 1 , 7 , 6 ) on the line passing through the points ( 2 , − 5 , 11 ) and ( − 6 , 7 , − 5 ) . Then t

Question

Let P be the point ( 10 , − 2 , − 1 ) and Q be the foot of the perpendicular drawn from the point R ( 1 , 7 , 6 ) on the line passing through the points ( 2 , − 5 , 11 ) and ( − 6 , 7 , − 5 ) . Then the length of the line segment PQ is equal to ________

TestHub · Accepted Answer

Line : − 8 x + 6 ​ = 12 y − 7 ​ = − 16 z + 5 ​ ​ 2 x + 6 ​ = − 3 y − 7 ​ = 4 z + 5 ​ = λ Q ( 2 λ − 6 , 7 − 3 λ , 4 λ − 5 ) QR ​ ( 2 λ − 7 , − 3 λ , 4 λ − 11 ) QR ​ ⋅ dr’s of line = 0 4 λ − 14 + 9 λ + 16 λ − 44 = 0 29 λ = 58 ⇒ λ = 2 Q ( − 2 , 1 , 3 ) PQ = 144 + 9 + 16 ​ = 169 ​ = 13 ​

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