Question
In: Advanced Math
Find the vector and parametric equations for the plane. The plane that contains the lines r1(t)...
Find the vector and parametric equations for the plane. The plane that contains the lines r1(t) = <6, 8, 8,> + t<-2, 9, 6> and r2 = <6, 8, 8> + t<5, 1, 7>.
Solutions
Colby Messinger answered 2 years agoRelated Solutions
There are an infinite number of vector and parametric equations for a given plane. Why is...
There are an infinite number of vector and parametric equations
for a given plane. Why is the scalar equation of a given plane
unique?
Find a vector equation and parametric equations for the line. (Use the parameter t.) The line...
Find a vector equation and parametric equations for the line.
(Use the parameter t.)
The line through the point
(2, 2.9, 3.6)
and parallel to the vector
3i + 4j − k
r(t)
=
(x(t), y(t), z(t))
=
Find the distance between the skew lines with parametric equations x = 1 + t, y...
Find the distance between the skew lines with parametric
equations x = 1 + t, y = 3 +
6t, z = 2t, and
x = 1 + 2s, y = 6 + 15s, z
= −2 + 6s.
Find the equation of the line that passes through the points on
the two lines where the shortest distance is measured.
Find the equation of the tangent plane and the parametric equations for the normal line to...
Find the equation of the tangent plane and the
parametric equations for the normal line to the surface
x2 + y2 - z = 0 at the point P(4,-1, 6).
Show all steps
Find the distance between the skew lines with the given parametric equations. x = 2 +...
Find the distance between the skew lines with the given
parametric equations.
x = 2 + t, y = 3 +
6t, z = 2t
x = 1 + 4s, y = 5 +
15s, z = -2 + 6s.
1. Given parametric equations below, find the values of t where the the parametric curve has...
1. Given parametric equations below, find the values of t where
the the parametric curve has a horizontal and vertical
tangents.
a) x=t^2 - t, y= t^2 + t
b) x= e^(t/10)cos(t), y= e^(t/10)sin(t)
2. Find the arc length of the graph of the parametric equations
on the given intervals.
a) x= 4t+2, y = 1-3t , −1 ≤ t ≤ 1
b) x= e^(t/10)cos(t), y= e^(t/10)sin(t), 0 ≤ t ≤ 2π
Find parametric equations for the tangent line to the curve with the given parametric equations at...
Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point.
Find all horizontal and vertical tangent lines for the parametric curve defined by x(t) = t^3...
Find all horizontal and vertical tangent lines for the
parametric curve defined by x(t) = t^3 - 3t +1, y(t) = 4t^2 +5.
then write our the equations for the tangent lines
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.$$ x=e^{-t} \cos t, \quad y=e^{-t} \sin t, \quad z=e^{-t} ; \quad(1,0,1) $$(b): Find the unit tangent vector \(\mathbf{T}\), the principal unit normal \(\mathbf{N}\), and the curvature \(\kappa\) for the space curve,$$ \mathbf{r}(t)=<3 3="" 4="" sin="" cos="" t="">$$
(a) Find the cosine of the angle between the lines L1 and L2 whose vector equations are given below:
(a) Find the cosine of the angle between the lines L1 and L2 whose vector equations are given below:
L1 : ~r1(t) = [1, 1, 1] + t[1, 2, 3]
L2 : ~r2(t) = [1, 1, 1] + t[−1, 4, 2].
(b) Find the equation of the plane that contains both L1 and L2.
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