If x² + y² + z² = 3, where x, y and z are integers, then how many values can (xy + yz + zx) have?
Two
Given x² + y² + z² = 3. Since x, y, z are integers, the possible values are: (1, 1, 1), (1, -1, 1), (1, 1, -1), (1, -1, -1), (-1, 1, 1), (-1, -1, 1), (-1, 1, -1), (-1, -1, -1) If (x, y, z) = (1, 1, 1), xy + yz + zx = 3 If (x, y, z) = (1, 1, -1), xy + yz + zx = 1 - 1 - 1 = -1 If (x, y, z) = (1, -1, -1), xy + yz + zx = -1 + 1 -1 = -1 If (x, y, z) = (-1, -1, -1), xy + yz + zx = -3
If α is the angle between the line joining P and Q, and the line joining P and R, then what is cos α equal to?
Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).