Let in a △ A BC , the length of the side A C be 6 , the vertex B be ( 1 , 2 , 3 ) and the vertices A , C lie on the line 3 x − 6 = 2 y − 7 = − 2 z − 7 . Then the area (in sq. units) of △ ABC is:

Question

Let in a △ A BC , the length of the side A C be 6 , the vertex B be ( 1 , 2 , 3 ) and the vertices A , C lie on the line 3 x − 6 ​ = 2 y − 7 ​ = − 2 z − 7 ​ . Then the area (in sq. units) of △ ABC is:

TestHub · Accepted Answer

​ Let M ( 3 λ + 6 , 2 λ + 7 , − 2 λ + 7 ) BM = ( 3 λ + 5 ) i ^ + ( 2 λ + 5 ) j ^ ​ + ( − 2 λ + 4 ) k ^ AC ⋅ BM = 0 = 3 ( 3 λ + 5 ) + 2 ( 2 λ + 5 ) − 2 ( − 2 λ + 4 ) BM = 2 i ^ + 3 j ^ ​ + 6 k ^ ∣ BM = 7 Area = 2 1 ​ × 6 × 7 = 21 ​

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