Assume that points A(5, 10, 1), B(6, 3, 6), and C(12, 1, 4) are on a plane.
Find vector AB and vector AC.
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To find vector AB, we subtract the coordinates of point A from the coordinates of point B.
Vector AB = B - A = (6 - 5, 3 - 10, 6 - 1) = (1, -7, 5)
To find vector AC, we subtract the coordinates of point A from the coordinates of point C.
Vector AC = C - A = (12 - 5, 1 - 10, 4 - 1) = (7, -9, 3)
So, vector AB is (1, -7, 5) and vector AC is (7, -9, 3).