+0  
 
-1
87
2
avatar+82 

done

 Mar 20, 2020
edited by rubikx2910  Apr 15, 2020
 #1
avatar+111360 
+3

This doesn't  work much differently than in 2 space.....we can still use the Law of Cosines

 

BC  = sqrt [ (2 - 4)^2  + (-2 -4)^2  + (2 - 4)^2 ]  = sqrt [ 4 + 36 + 4]  = sqrt (44)

AC = sqrt [ (1 - 4)^2 + (0 - 4)^2 + (2 - 2)^2] = sqrt ( 9 + 16)  = sqrt (25)   =5

AB = sqrt [ (1 - 2)^2 + (-2 - 0)^2 + ( 4 - 2)^2 ]  = sqrt [ 1 + 4 + 4 ] =  sqrt (9)  = 3

 

So....we have  that

 

BC^2  = AC^2 + AB^2  - 2 ( AC)(AB) cos (BAC)

 

44 = 25 + 9  - 2 (5)(3) cos (BAC)

 

[44 - 25 - 9]  / [ -2 * 5 * 3 ]  = cos (BAC)

 

cos (BAC)  =   10 / [ - 30 ]  =  -1/3

 

 

cool cool cool

 Mar 20, 2020
 #2
avatar+82 
+1

done

rubikx2910  Mar 20, 2020
edited by rubikx2910  Apr 15, 2020

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