Statement 1 - Let A , B , C be points with position vectors r 1 = 2 i ^ − j ^ + k ^ , r 2 = i ^ + 2 j ^ + 3 k ^ and r 3 = 3 i ^ + j ^ + 2 k ^ relative to the origin O . The shortest distan

Question

Statement 1 - Let A , B , C be points with position vectors r 1 ​ = 2 i ^ − j ^ ​ + k ^ , r 2 ​ = i ^ + 2 j ^ ​ + 3 k ^ and r 3 ​ = 3 i ^ + j ^ ​ + 2 k ^ relative to the origin O . The shortest distance between the point B and the plane O A C is 5/7 ​ . Statement 2 - Shortest distance = ∣ O A × OC ∣ ∣ ( O A × OC ) ⋅ OB ∣ ​ .

TestHub · Accepted Answer

O A × OC = ( 2 , − 1 , 1 ) × ( 3 , 1 , 2 ) = ( − 3 , − 1 , 5 ) , magnitude 35 ​ ⋅ OB . ( − 3 , − 1 , 5 ) = − 3 − 2 + 15 = 10 . Distance = 35 ​ 10 ​ = 7 20 ​ ​  = 7 5 ​ ​ , so Statement 1 is false. Statement 2 is the correct formula, so it is true.

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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