diketahui A (4, 7, 0), B (6, 10, -6), dan C (x, 9, 0) agar sudut BAC = 90, maka nilai x adalah

|BC|^2 = |AB|^2 + |AC|^2
(x-6)^2 + (9-10)^2 + (0-(-6))^2 = ( (6-4)^2 + (10-7)^2 + (-6-0)^2 ) + ( (x-4)^2 + (9-7)^2 + (0-0)^2 )
(x-6)^2 + (-1)^2 + (6)^2 = ( (2)^2 + (3)^2 + (-6)^2 ) + ( (x-4)^2 + (2)^2 + (0)^2 )
(x-6)^2 + 1 + 36 = ( 4 + 9 + 36 ) + ( (x-4)^2 + 4 + 0 )
(x-6)^2 + 37 = ( 49 ) + ( (x-4)^2 + 4 )
(x-6)^2 + 37 = (x-4)^2 + 53
(x-6)^2 - (x-4)^2 =  53 - 37
x^2 - 12x + 4 - x^2 + 8x - 16 = 16
-4x - 12 = 16
-4x = 28
x = 28/-4
x = -7