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 dri [r₁(t) · r₂(t)] = r₁(t). + r₂(t) and dt dt dt d dr₂ dri [r₁(t) × r₂(t)] = r₁(t) × + x r₂(t). dt dt dt r₁(t) = cos(t)i + sin(t)j + 3tk, r₂(t) = 2i + tk d dt = [r₁(t) · r₂(t)] = = d dt [r₁(t) × r₂(t)] =

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[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)] = r1₁(t). +
r₂(t) and
dt
dt dt
d
dr₂
dri
[r₁(t) × r₂(t)] = r₁(t) × + x r₂(t).
dt
dt
dt
r₁(t) = cos(t)i + sin(t)j + 3tk, r₂(t) = 2i + tk
d
dt
[
d
dt
[r₁(t) · r₂(t)] =
=
;[r₁(t) × r₂(t)]:
=
.
Transcribed Image Text:d d Calculate[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)] = r1₁(t). + r₂(t) and dt dt dt d dr₂ dri [r₁(t) × r₂(t)] = r₁(t) × + x r₂(t). dt dt dt r₁(t) = cos(t)i + sin(t)j + 3tk, r₂(t) = 2i + tk d dt [ d dt [r₁(t) · r₂(t)] = = ;[r₁(t) × r₂(t)]: = .
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