d Calculate =[rı(t) · r₂(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly and then by applying the formulas drit). . dr₂ dr₁ + dt dt [r₁(t) · r₂(t)] = r₁(t) · . r₂(t) and d dr₂ dri ·[r₁(t) × r₂(t)] = r₁(t) × ri(t) + x r₂(t). dt dt dt r₁(t) = cos(t)i + sin(t)j + 4tk, r₂(t) = 3i + tk [r₁(t) · r₂(t)] [r₁(t) × r₂(t)] dt d dt = = [

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 76E
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Question
d
d
Calculate
77[r1(t) · r2(t)] and r₁(t) × r₂(t)] first by differentiating
dt
dt
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 + x r₂(t).
dt
dt dt
r₁(t)
cos(t)i + sin(t)j + 4tk,
r₂(t) = 3i + tk
d
dt
[ri(t) · r₂(t)]
- = [
d
dt
[r₁(t) × r2(t)] =
=
Transcribed Image Text:d d Calculate 77[r1(t) · r2(t)] and r₁(t) × r₂(t)] first by differentiating dt dt 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 + x r₂(t). dt dt dt r₁(t) cos(t)i + sin(t)j + 4tk, r₂(t) = 3i + tk d dt [ri(t) · r₂(t)] - = [ d dt [r₁(t) × r2(t)] = =
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