Let the vertices Q and R of the triangle PQR lie on the line 5 x + 3 = 2 y − 1 = 3 z + 4 , QR = 5 and the coordinates of the point P be ( 0 , 2 , 3 ) . If the area of the triangle PQR is n m t

Question

Let the vertices Q and R of the triangle PQR lie on the line 5 x + 3 ​ = 2 y − 1 ​ = 3 z + 4 ​ , QR = 5 and the coordinates of the point P be ( 0 , 2 , 3 ) . If the area of the triangle PQR is n m ​ then :

TestHub · Accepted Answer

M ( 5 λ − 3 , 2 λ + 1 , 3 λ − 4 ) Drs of PM ⇒ 5 λ − 3 , 2 λ − 1 , 3 λ − 7 Drs of line L ⇒ 5 , 2 , 3 PM ⊥ L ⇒ ( 5 λ − 3 ) 5 + ( 2 λ − 1 ) 2 + ( 3 λ − 7 ) 3 = 0 ⇒ λ = 1 ∴ M ( 2 , 3 , − 1 ) PM = 4 + 1 + 16 ​ = 21 ​ Area = 2 1 ​ × 5 × 21 ​ = n m ​ 2 m − 5 21 ​ n = 0

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