d d Calculateri(t) r2(t)] and 77[r1(t) × r²(t)] first by differentiating the product directly and then by applying the formulas d. dr₂ dr₁ [r₁(t) · r2(t)] = r₁(t) · + r₂(t) and dt dt dt d dr₂ dri [r₁(t) × r2(t)] = r₁(t) × · + x r₂(t). dt dt dt r₁(t) = cos(t)i + sin(t)j + 2tk, r₂(t) = i + tk d dt dt [r₁(t) · r₂(t)] = [ = [r₁(t) × r2(t)] : =

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 17EQ
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Question
d
Calculate
d
dt
[ri(t)
· r₂(t)]
[ri(t) · r2(t)] and
and[r₁(t) × r₂(t)] first by differentiating
dt
the product directly and then by applying the formulas
d
dr2
dri
[r₁(t) · r2(t)] = r₁(t) ·
+ r₂(t) and
dt
dt
dt
d
dr₂
dri
[r₁(t) × r₂(t)] = r₁(t) × + x r₂(t).
dt
dt
dt
r₁(t) = cos(t)i + sin(t)j + 2tk, r₂(t) = i + tk
d
dt
=
[r₁(t) · r₂(t)] =
|
d
dt
[r₁(t) = r₂(t)] = [
Transcribed Image Text:d Calculate d dt [ri(t) · r₂(t)] [ri(t) · r2(t)] and and[r₁(t) × r₂(t)] first by differentiating dt the product directly and then by applying the formulas d dr2 dri [r₁(t) · r2(t)] = r₁(t) · + r₂(t) and dt dt dt d dr₂ dri [r₁(t) × r₂(t)] = r₁(t) × + x r₂(t). dt dt dt r₁(t) = cos(t)i + sin(t)j + 2tk, r₂(t) = i + tk d dt = [r₁(t) · r₂(t)] = | d dt [r₁(t) = r₂(t)] = [
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