Let P be the image of the point Q ( 7 , − 2 , 5 ) in the line L : 2 x − 1 = 3 y + 1 = 4 z and R ( 5 , p , q ) be a point on L . Then the square of the area of △ PQR is ________.

Question

Let P be the image of the point Q ( 7 , − 2 , 5 ) in the line L : 2 x − 1 ​ = 3 y + 1 ​ = 4 z ​ and R ( 5 , p , q ) be a point on L . Then the square of the area of △ PQR is ________.

TestHub · Accepted Answer

​ Let R ( 2 λ + 1 , 3 λ − 1 , 4 λ ) 2 λ + 1 = 5 λ = 2 R ( 5 , 5 , 8 ) let T ( 2 λ + 1 , 3 λ − 1 , 4 λ ) QT ​ = ( 2 λ − 6 ) i ^ + ( 3 λ + 1 ) j ^ ​ + ( 4 λ − 5 ) k ^ b = 2 i ^ + 3 j ^ ​ + 4 k ^ QT ​ ⋅ b = 0 4 λ − 12 + 9 λ + 3 + 16 λ − 20 = 0 ​ ​ λ = 1 T ( 3 , 2 , 4 ) QT = 33 ​ RT = 29 ​ ( area of Δ PQR ) 2 = ( 2 1 ​ 29 ​ ⋅ 2 33 ​ ) 2 = 957 ​

Mathematics - Vector Question with Solution | TestHub

Doubts & Discussion