Question

Find the point at which the line intersects the given plane.

x = -t+8 , y= 2t-2, z=6 Plane: x-4y=-6

Answer #1

x=-t+8

y=2t-2

z=6

The plane is

**therefore the point at which they intersect is
**

Determine whether the line (x,y,z) = r(t) = (1-t, 4-5t,
2t+5)
a. Intersects the xy plane
b. Intersects with the z-axis

Consider plane P: 4x -y + 2z = 8, line: <x, y, z> =
<1+t, -1+2t, 3t>, and point Q(2,-1,3)
b) Find the perpendicular distance between point Q and plane
P

(a) Find the equation of the plane p containing the point
P(1,3,2)and normal to the line l which has parametric form
x=2,y=t+1,z=2 t+4.
Put x, y and z on the left hand side and the constant on the
right-hand side.
(b) Find the value of t where the line l intersects the plane
p.
(c) Enter the coordinates of the point where the line l
intersects the plane p.

Find the equation for the line through the point (2,0,2),
parallel to the plane x+y+z=10 and orthogonal to the line
r(t)=<1+t,1-t,2t>

find the distance between the point (-1,3,5) and the line given
by x=5+t, y=3-2t, and z=1-t

Find equations of the normal plane and osculating plane of the
curve at the given point
x = sin(2t), y = t, z = cos(2t)
at (0, pi, 1)

The paraboloid
z = 5 − x −
x2 −
2y2
intersects the plane x = 4 in a parabola. Find
parametric equations in terms of t for the tangent line to
this parabola at the point
(4, 2, −23).
(Enter your answer as a comma-separated list of equations. Let
x, y, and z be in terms of
t.)

The paraboloid z = 5 − x − x2 − 2y2 intersects the plane x = 1
in a parabola. Find parametric equations in terms of t for the
tangent line to this parabola at the point (1, 4, −29). (Enter your
answer as a comma-separated list of equations. Let x, y, and z be
in terms of t.)

find the parametric equation of the line passing through the
point (1,7,2), parallel to the plane x+y+z=2 and perpendicular to
the line x=2t, y=(3t+5)2, and z=(4t-1)/3

1. Find the distance between the point and the line given by the
set of parametric equations. (Round your answer to three decimal
places.)
(8, -1, 4); x = 2t, y = t −
3, z = 2t + 2
I had put 6.87 but it shows as it being wrong.
2. Consider the following planes.
−6x + y + z
=
6
24x − 4y + 6z
=
36
Find the angle between the two planes. (Round your answer...

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