If θ is the angle between the lines A B , A C where A , B , C are the three points with coordinates ( 1 , 2 , − 1 ) , ( 2 , 0 , 3 ) , ( 3 , − 1 , 2 ) respectively then 231 cos θ =

Question

If θ is the angle between the lines A B , A C where A , B , C are the three points with coordinates ( 1 , 2 , − 1 ) , ( 2 , 0 , 3 ) , ( 3 , − 1 , 2 ) respectively then 231 ​ cos θ =

TestHub · Accepted Answer

It is easy to see A B = i − 2 j + 4 k ; A C = 2 i − 3 j + 3 k A B ⋅ A C = 20 A B ⋅ A B = 21 , A C ⋅ A C = 22 Thus cos θ = ∣ A B ∣ A C ∣ A B ⋅ A C ​ = 462 ​ 20 ​ = 231 ​ cos θ = 10 2 ​ = 14.14

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