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.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text: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 (v x 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.
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Follow-up Question
can you show how do you calculate for these two parts?
Transcribed Image Text:=(i + (cos t)j + (− sin t)k) × ((3t)i + 2k) + ((t)i + (sin t)j + (cos t)) × (3i + 0k)
i
j
ki
j
k
cos tsin t+t
sin t
1
3t 0
2
3 0 0
=(2 cos t)i + (−2 − 3t sin t)j + (−3t cos t)k + 0i+ (3 cos t)j + (−3 sin t)k
cos t
Transcribed Image Text:Since,
v (t) x w (t)=((t)i
+ (sin t)j + (cos t)k) x ((3t)i + 2k)
k
i
t
cos t
3t 0
2
=(2 sin t)i + (3t cos t − 2t)j + (−3t sin t)k
j
sint
Solution
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