3. Let i, j, k denote the unit vectors along the three coordinate axes. Let v(t) = ti + sintj + costk and w(t) = 3ti + 2k. (a) Compute (v.w)'(t) directly and check your answer by using the product rule (for the dot product, stated in the class). Note that the dot above, is the dot product of vectors and' denotes the derivative. (b) Compute (vx w)'(t) directly and check your answer by using the product rule (for the cross product, again stated in the class). Note that the x above, is the cross product of vectors.

3. Let i, j, k denote the unit vectors along the three coordinate axes. Let v(t) = ti + sintj + costk and w(t) = 3ti + 2k. (a) Compute (v.w)'(t) directly and check your answer by using the product rule (for the dot product, stated in the class). Note that the dot above, is the dot product of vectors and' denotes the derivative. (b) Compute (vx w)'(t) directly and check your answer by using the product rule (for the cross product, again stated in the class). Note that the x above, is the cross product of vectors.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 12E

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