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Problem 1.1 Prove the Vector Triple Product rule by writing out both sides in component form A x (B x C) = B(A · C) – C(A · B) %3D Problem 1.2 Find the gradient of the following functions a) f(x, y, z) = x² + y³ + z4 %3D b) f(x, y, z) = x²y³24 c) f(x, y, z) = eª sin y ln z

Problem 1.1 Prove the Vector Triple Product rule by writing out both sides in component form A x (B x C) = B(A · C) – C(A · B) %3D Problem 1.2 Find the gradient of the following functions a) f(x, y, z) = x² + y³ + z4 %3D b) f(x, y, z) = x²y³24 c) f(x, y, z) = eª sin y ln z

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Problem 1.3 Let A be the separation vector from a fixed point (', y', 2) to the point (*, Y, z), and let A be its length. Show that, V(A?) = 2A
Transcribed Image Text:Problem 1.3 Let A be the separation vector from a fixed point (', y', 2) to the point (*, Y, z), and let A be its length. Show that, V(A?) = 2A
Problem 1.1 Prove the Vector Triple Product rule by writing out both sides in component form A x (B × C) = B(A · C) – C(A · B) Problem 1.2 Find the gradient of the following functions a) f(x, y, z) = x² + y³ + z4 = x + y° + z* ,234 b) f(x, y, z) = x²y³zª f (x, y, z) = e" sin y ln z c)
Transcribed Image Text:Problem 1.1 Prove the Vector Triple Product rule by writing out both sides in component form A x (B × C) = B(A · C) – C(A · B) Problem 1.2 Find the gradient of the following functions a) f(x, y, z) = x² + y³ + z4 = x + y° + z* ,234 b) f(x, y, z) = x²y³zª f (x, y, z) = e" sin y ln z c)
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