1) Consider a vector field à (x, y, z) and a scalar field v (x, y, z) which are defined as Ã(x, y, z) = (3y²z² – 1)ê + (4x²z³ + 1)ŷ + (5a²y³ – 2)2 and V(x, y, z) = 5x² + 7y² + 9z², respectively. Compute the following quantites: a) V. Ā. Is this quantity a vector or a scalar? b) V x Ã. Is this quantity a vector or a scalar? c) V b. Is this quantity a vector or a scalar?
1) Consider a vector field à (x, y, z) and a scalar field v (x, y, z) which are defined as Ã(x, y, z) = (3y²z² – 1)ê + (4x²z³ + 1)ŷ + (5a²y³ – 2)2 and V(x, y, z) = 5x² + 7y² + 9z², respectively. Compute the following quantites: a) V. Ā. Is this quantity a vector or a scalar? b) V x Ã. Is this quantity a vector or a scalar? c) V b. Is this quantity a vector or a scalar?
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Transcribed Image Text:1) Consider a vector field à (x, y, z) and a scalar field v (x, y, z) which are defined as
Ã(x, y, z) = (3y²z² – 1)ê + (4x²z³ + 1)ŷ + (5a²y³ – 2)2
and
V(x, y, z) = 5x² + 7y² + 9z²,
respectively. Compute the following quantites:
a) V. Ā. Is this quantity a vector or a scalar?
b) V x Ã. Is this quantity a vector or a scalar?
c) V b. Is this quantity a vector or a scalar?
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