d [r1(t) · r2(t)] dt d [ri(t) x r₂(t)] dt = =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 46E
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Question
d
d
Calculate[ri(t) · r₂(t)] and
dt
ar(t).
[r₁(t) × r₂(t)] first by differentiating
dt
the product directly and then by applying the formulas
d
dr2 dr₁
77[r₁(t) · r2(t)] = r1(t) · +
.
r₂(t) and
dt
dt dt
d
dr₂ dr₁
77[r₁(t) × r₂(t)] = r₁(t) × + x r₂(t).
dt
dt dt
r₁(t) = cos(t)i + sin(t)j +8tk, r₂(t) = 7i + tk
d
dt
d
dt
[ri(t) r₂(t)]
·
[r₁(t) × r₂(t)] :
=
=
Transcribed Image Text:d d Calculate[ri(t) · r₂(t)] and dt ar(t). [r₁(t) × r₂(t)] first by differentiating dt the product directly and then by applying the formulas d dr2 dr₁ 77[r₁(t) · r2(t)] = r1(t) · + . r₂(t) and dt dt dt d dr₂ dr₁ 77[r₁(t) × r₂(t)] = r₁(t) × + x r₂(t). dt dt dt r₁(t) = cos(t)i + sin(t)j +8tk, r₂(t) = 7i + tk d dt d dt [ri(t) r₂(t)] · [r₁(t) × r₂(t)] : = =
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