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d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating d dt the product directly and then by applying the formulas dt d dr2 dri Ir.(t) - ra(t)) = ri(t)- + r2(t) and dt dt dt d [r:(t) × r2(t)] = ri(t) × dr2 dri x r2(t). %3| dt dt dt ri(t) = cos(t)i+ sin(t)j+ 2tk, r2(t) = i+ tk d ri(t) · r2(t)] dt d d ri(t) x r2(t)]

d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating d dt the product directly and then by applying the formulas dt d dr2 dri Ir.(t) - ra(t)) = ri(t)- + r2(t) and dt dt dt d [r:(t) × r2(t)] = ri(t) × dr2 dri x r2(t). %3| dt dt dt ri(t) = cos(t)i+ sin(t)j+ 2tk, r2(t) = i+ tk d ri(t) · r2(t)] dt d d ri(t) x r2(t)]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 dt d ri(t) • r2(t)] = r1(t) - dr2 dri + dt dt r2(t) and dt d ri(t) x r2(t)] = ri(t) x dr2 dr1 + dt x r2(t). dt dt r1(t) = cos(t)i + sin(t)j+ 2tk, r2(t) = i+ tk d ri(t) · r2(t)] : dt d r:(t) x r2(t)] %3D
Transcribed Image Text: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 dt d ri(t) • r2(t)] = r1(t) - dr2 dri + dt dt r2(t) and dt d ri(t) x r2(t)] = ri(t) x dr2 dr1 + dt x r2(t). dt dt r1(t) = cos(t)i + sin(t)j+ 2tk, r2(t) = i+ tk d ri(t) · r2(t)] : dt d r:(t) x r2(t)] %3D
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