Let U be a vector function of position in R3 with continuous second partial deriva- tives. We write (U₁, U2, U3) for the components of U. (a) Show that ¹⁄▼ (Ü · Ü) – Ü × (▼ × Ü) = (Ũ · ▼) Ū, where ((UV)U), = U₁ (b) We define the vector function of position, by setting = V × . If the condition V U = 0 holds true, show that ▼ × ((Ū · ▼) Ú) = (Ū · ▼) Ñ — (Ñ · ▼) Ú. . (Hint: The representation of (UV) U from the first part might be useful.)

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