d d Calculate (ri(t) · r2(t)] and [ri(t) x r2(t)] first by differentiating dt the product directly and then by applying the formulas dr2 dri d [ri(t) r2(t)] = ri(t). r2(t) and dt %3D dt dt d dr2 = r1(t) x dri di ri(t) × r2(t)] x r2(t). dt dt r1(t) : cos(t)i + sin(t)j + 5tk, r2(t) = 4i + tk

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 20EQ
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d
Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating
dt
dt
the product directly and then by applying the formulas
d
[ri(t) r2(t)] = ri(t) ·
dr2
+
dt
dri
· r2(t) and
%3|
dt
dt
d
dr2
dri
[ri(t) x r2(t)] = r1(t) ×
x r2(t).
dt
+
dt
dt
r1(t) = cos(t)i+ sin(t)j + 5tk,
r2(t) = 4i + tk
d
dt
d
[ri(t) x r2(t)] :
dt
Transcribed Image Text:d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly and then by applying the formulas d [ri(t) r2(t)] = ri(t) · dr2 + dt dri · r2(t) and %3| dt dt d dr2 dri [ri(t) x r2(t)] = r1(t) × x r2(t). dt + dt dt r1(t) = cos(t)i+ sin(t)j + 5tk, r2(t) = 4i + tk d dt d [ri(t) x r2(t)] : dt
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