Let c be a scalar, a and b be vectors, and X (x, y, z) Show that the equation (X a) (X b) c 2 defines a sphere with center m 1 2 (a b) and radius R, where R 2 c 2 1 2 (a b) 2

Question: Let c be a scalar, a and b be vectors, and X = (x, y, z). Show that the equation (X a) (X

Let c be a scalar, a and b be vectors, and X = (x, y, z). Show that the equation (X − a) · (X − b) = c² defines a sphere with center m = 1/2 (a + b) and radius R, where R² = c² + ΙΙ1/2 (a − b)ΙΙ².

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