If l i 2 + m i 2 + n i 2 = 1∀ i ∈ { 1 , 2 , 3 } and l i l j + m i m j + n i n j = 0∀ i , j ∈ { 1 , 2 , 3 } ( i  = j ) , Δ = l 1 l 2 l 3 m 1 m 2 m 3 n 1 n 2 n 3

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If l i 2 ​ + m i 2 ​ + n i 2 ​ = 1∀ i ∈ { 1 , 2 , 3 } and l i ​ l j ​ + m i ​ m j ​ + n i ​ n j ​ = 0∀ i , j ∈ { 1 , 2 , 3 } ( i  = j ) , Δ = ​ l 1 ​ l 2 ​ l 3 ​ ​ m 1 ​ m 2 ​ m 3 ​ ​ n 1 ​ n 2 ​ n 3 ​ ​ ​ , then

TestHub · Accepted Answer

Δ 2 = Δ ⋅ Δ T is the determinant of the matrix of dot products of the rows, which is the identity matrix. So Δ 2 = 1 and ∣Δ∣ = 1 .

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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