Let ABCD be a tetrahedron in which position vectors of A, B, C and D are i ^ + j ^ + k ^ , 2 i ^ + j ^ + 2 k ^ , 3 i ^ + 2 j ^ + k ^ and 2 i ^ + 3 j ^ + 2 k ^ . If ABC be the base of the tetra

Question

Let ABCD be a tetrahedron in which position vectors of A, B, C and D are i ^ + j ^ ​ + k ^ , 2 i ^ + j ^ ​ + 2 k ^ , 3 i ^ + 2 j ^ ​ + k ^ and 2 i ^ + 3 j ^ ​ + 2 k ^ . If ABC be the base of the tetrahedron then the height of the tetrahedron is

TestHub · Accepted Answer

A B × A C = ( 1 , 0 , 1 ) × ( 2 , 1 , 0 ) = − i ^ + 2 j ^ ​ + k ^ and A D = ( 1 , 2 , 1 ) . Height = ∣ A B × A C ∣ ∣ A D ⋅ ( A B × A C ) ∣ ​ = 6 ​ 4 ​ = 3 ​ 2 2 ​ ​ .

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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