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d Calculate[ri(t) · r2(t)] and 77[r1(t) × r2(t)] first by differentiating @[r₁(t) 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 dr₁ [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. [r₁(t) · ri(t) r₂(t)] -4 t - sin(t) = dt d -[r₁(t) × r₂(t)] = (sin(t) + t cos(t)) i+t sin(t) — cos(t) + 2 − cos(t) k dt

d Calculate[ri(t) · r2(t)] and 77[r1(t) × r2(t)] first by differentiating @[r₁(t) 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 dr₁ [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. [r₁(t) · ri(t) r₂(t)] -4 t - sin(t) = dt d -[r₁(t) × r₂(t)] = (sin(t) + t cos(t)) i+t sin(t) — cos(t) + 2 − cos(t) k dt

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 27E
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Your answer is partially correct. d d Calculate[ri(t) · [r₁(t) · r2(t)] and @[r₁(t) × r2(t)] first by differentiating the product directly and then by applying the formulas dr₂ dr₁ [r₁(t) · r₂(t)] = r₁(t) · + r₂(t) and dt dt dt d dr2 dr₁ -[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 [r₁(t) · r₂(t)] 4 t - sin(t) dt d [r₁(t) × r₂(t)] = (sin(t) +t cos(t)) i + t sin(t) − cos(t) + 2 − cos(t) k dt = .
Transcribed Image Text:Your answer is partially correct. d d Calculate[ri(t) · [r₁(t) · r2(t)] and @[r₁(t) × r2(t)] first by differentiating the product directly and then by applying the formulas dr₂ dr₁ [r₁(t) · r₂(t)] = r₁(t) · + r₂(t) and dt dt dt d dr2 dr₁ -[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 [r₁(t) · r₂(t)] 4 t - sin(t) dt d [r₁(t) × r₂(t)] = (sin(t) +t cos(t)) i + t sin(t) − cos(t) + 2 − cos(t) k dt = .
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