If u = 3y^2ex − xey + 5ez, v = xex + (y − z)ey, and a = 5x^3 − y + yz, evaluate:(a) u·v (b) u×v (c) ∇×v (d) ∇a (e) ∇·uBased on your answers above, evaluate the following true/false assertions:(a) The dot product of two vectors is a scalar.(b) The cross product of two vectors is a scalar.(c) The curl of a vector is a vector.(d) The gradient of a scalar is a scalar.(e) The divergence of a vector is a scalar

If u = 3y^2ex − xey + 5ez, v = xex + (y − z)ey, and a = 5x^3 − y + yz, evaluate:(a) u·v (b) u×v (c) ∇×v (d) ∇a (e) ∇·uBased on your answers above, evaluate the following true/false assertions:(a) The dot product of two vectors is a scalar.(b) The cross product of two vectors is a scalar.(c) The curl of a vector is a vector.(d) The gradient of a scalar is a scalar.(e) The divergence of a vector is a scalar

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 31E

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