d d Calculate ri(t) · r2(t)] and [ri(t) × r2(t)] first by differentiating dt the product directly and then by applying the formulas d dri dr2 [r:(t) • r2(t)] = r1(t) · r2(t) and dt dt dt dr2 + [r1(t) × r2(t)] = r1(t) × dt dt d dri x r2(t). dt ri(t) = cos(t)i + sin(t)j+ 8tk, r2(t) = 7i + tk d ri(t) · r2(t)] dt d. [r(t) x r2(t)] : dt

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 4E: Let A=[aij]23 where aij=i+j, and let B=[bij]34 where bij=2ij. If AB=[cij]24, write a formula for cij...
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d.
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
dr2
dr1
[r:(t) · r2(t)] = r;(t) -
r2(t) and
dt
dt
dt
d
ri(t) x r2(t)] =r;(t) x
dr2
dri
x r2(t).
dt
dt
dt
ri(t) = cos(t)i + sin(t)j+ 8tk,
r2(t) = 7i + tk
d
diri(t) · r2(t)] =
d
d r: (t) x r2(t)]
Transcribed Image Text:d. 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 dr2 dr1 [r:(t) · r2(t)] = r;(t) - r2(t) and dt dt dt d ri(t) x r2(t)] =r;(t) x dr2 dri x r2(t). dt dt dt ri(t) = cos(t)i + sin(t)j+ 8tk, r2(t) = 7i + tk d diri(t) · r2(t)] = d d r: (t) x r2(t)]
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