d Calculate [ri(t) r2(t)] and [ri(t) x r2(t)] first by differentiating d't dt the product directly and then by applying the formulas

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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Calculateri(t) r2(t)] and 1 de dri(t):
the product directly and then by applying the formulas
d
dr₂ dr₁
[ri(t) r₂(t)] = r₁(t). + r₂(t) and
dt
dt
dt
d
dr2
dr₁
[r₁(t) × r₂(t)] = r₁(t) x
ri(t) >
+ x r₂(t).
dt
dt dt
r₁(t) = 4ti + 2t²j+5t³k, r₂(t) = t¹k
d
r₁(t) · r2(t)] = [35 + 6
X
dt
d
r₁(t) × r2(t)] = [12 + 5 i − 20+4 j| X
dt
[r₁(t) x r₂(t)] first by differentiating
Transcribed Image Text:Calculateri(t) r2(t)] and 1 de dri(t): the product directly and then by applying the formulas d dr₂ dr₁ [ri(t) r₂(t)] = r₁(t). + r₂(t) and dt dt dt d dr2 dr₁ [r₁(t) × r₂(t)] = r₁(t) x ri(t) > + x r₂(t). dt dt dt r₁(t) = 4ti + 2t²j+5t³k, r₂(t) = t¹k d r₁(t) · r2(t)] = [35 + 6 X dt d r₁(t) × r2(t)] = [12 + 5 i − 20+4 j| X dt [r₁(t) x r₂(t)] first by differentiating
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