High School
SAT
ACT
University
MCAT
LSAT
DAT

Given the following vector equation, sketch out the curve that it generates. r(…

Related Topics

Wize University Calculus 2 Textbook > Vector Functions

Vector Functions

3 Activities

checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Given the following vector equation, sketch out the curve that it generates.
r(t)=⟨cos⁡(t),t⟩r(t) = \langle \cos (t), t \rangle

More Vector Functions Questions:
3 The position of an object is given by
r⃗(t)=ln⁡(sin⁡t)i⃗−tk⃗\vec r(t) = \ln(\sin t)\vec i -t\vec k
for 0<t<π. 0 < t < \pi. Determine the minimum speed of the object.
2 The position of an object is given by
r⃗(t)=ln⁡(sin⁡t)i⃗−tk⃗\vec r(t) = \ln(\sin t)\vec i -t\vec k
Determine the velocity, acceleration, and speed at time t.
1 The position of an object is given by
r⃗(t)=etsin⁡ti⃗+etcos⁡tj⃗−etk⃗\vec r(t) = e^t\sin t\vec i + e^t\cos t\vec j-e^t\vec k
Determine the velocity, acceleration, and speed at time t.
Find the Cartesian equation of the tangent line to the following curve at the indicated point:
r⃗(t)=ln⁡(cos⁡t)i⃗+sin⁡(2t)j⃗−cos⁡2tk⃗ at t=π/6\vec r(t) = \ln(\cos t) \vec i + \sin(2t) \vec j- \cos^2 t \vec k\quad \text{ at } t = \pi/6
Practice: Domain of a vector-valued function 2
Find the domain of the following function. Express the domain as an interval, or a union of intervals. i.e. t∈[−3,3)t \in [-3, 3) or t∈(−∞,π]∪(13,∞)t \in (-\infty, \pi] \cup ( 13, \infty) .
v(x)=⟨x9x2−x4,−log⁡(−x3)⟩v(x) = \left \langle \frac{x}{\sqrt{9x^2 - x^4}}, - \log \left ( - \frac{x}{3} \right )\right \rangle
The following curves intersect when t=0t = 0 . What is the angle between these two curves:
r1(t)=⟨t,1+t2,cos⁡(t)+t⟩r2(t)=⟨sin⁡(t),cos⁡(t),et⟩r_1(t) = \langle t, 1 + t^2, \cos(t) + t \rangle \quad\quad\quad r_2(t) = \langle \sin(t), \cos(t), e^t \rangle
Let's say that a vector function r(t)r(t) that describes a curve CC has the property that for all tt , r(t)r(t) is perpendicular to its tangent vector. Demonstrate that the curve must be completely contained on the surface of a sphere centered at the origin.
Give at least one point where the following vector function
r(t)=⟨−sin⁡t,2et,−t⟩r(t) = \langle -\sin t, 2e^t, -t\rangle
has tangent vectors normal to the plane whose equation is