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d d Calculate ri(t) · r2(t)] and [r:(t). x r2(t)] first by differentiating dt dt the product directly and then by applying the formulas d dr2, dri [ri(t) · r2(t)] = r;(t) - r2(t) and dt dt dt dr2 + dt dri d ri(t) × r2(t)] = rị(t) × x r2(t). dt dt ri(t) = cos(t)i + sin(t)j+ 8tk, r2(t) = 7i + tk %3D d ri(t) - r2(t)] =| 16 t – 7 sin(t) dt d [ri(t) × r2(t)] =sin(t) +t cos(t) i – cos(t) + 56 +t sin(t) j – 7 cos(t) k

d d Calculate ri(t) · r2(t)] and [r:(t). x r2(t)] first by differentiating dt dt the product directly and then by applying the formulas d dr2, dri [ri(t) · r2(t)] = r;(t) - r2(t) and dt dt dt dr2 + dt dri d ri(t) × r2(t)] = rị(t) × x r2(t). dt dt ri(t) = cos(t)i + sin(t)j+ 8tk, r2(t) = 7i + tk %3D d ri(t) - r2(t)] =| 16 t – 7 sin(t) dt d [ri(t) × r2(t)] =sin(t) +t cos(t) i – cos(t) + 56 +t sin(t) j – 7 cos(t) k

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)
Problem 29E
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d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly and then by applying the formulas d. [ri(t) • r2(t)] = r1(t) · dr2 dri r2(t) and dt dt dt d dr2 dri ri(t) x r2(t)] = r1(t) × dt x r2(t). dt dt ri(t) = cos(t)i + sin(t)j+ 8tk, r2(t) = 7i + tk d ri(t) · r2(t)] = 16 t – 7 sin(t) dt d dlr: (t) x r2(t) : = sin(t) +t cos(t) i – cos(t) + 56 +t sin(t) j – 7 cos(t) k X1
Transcribed Image Text:d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly and then by applying the formulas d. [ri(t) • r2(t)] = r1(t) · dr2 dri r2(t) and dt dt dt d dr2 dri ri(t) x r2(t)] = r1(t) × dt x r2(t). dt dt ri(t) = cos(t)i + sin(t)j+ 8tk, r2(t) = 7i + tk d ri(t) · r2(t)] = 16 t – 7 sin(t) dt d dlr: (t) x r2(t) : = sin(t) +t cos(t) i – cos(t) + 56 +t sin(t) j – 7 cos(t) k X1
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