Question

shows that the 3x-6y + 2z = 5 plane is parallel to the line x = 1 +
9t, y = 5-4t, z = 9-t and calculates the distance between the
two

Answer #1

Find the equation of the tangent plane and normal line
to the curve 2z−5=ln( x 2 y 3 )− 6y x 2z−5=ln(x2y3)−6yx at
(1,e)

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

show that
L: x=-1+t , y=3+2t ,z=-t
and the plane P : 2x-xy-2z=-3
are parallel then find the distance btween them

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

Find the angle between the plane x+y+ 2z = 6 and the line x-1 =
y-3 = z+2

Find the parametric and symmetric equations of the line that is
parallel to the line x = 2 - 3t, y = 4 + t, z = -5 + 4t and passes
through the point (1, -4, 7)

a) Let T be the plane 3x-y-2z=9. Find the shortest distance d
from the point P0 = (5, 2, 1) to T, and the point Q in T that is
closest to P0. Use the square root symbol where needed.
d=
Q= ( , , )
b) Find all values of X so that the triangle with vertices A =
(X, 4, 2), B = (3, 2, 0) and C = (2, 0 , -2) has area (5/2).

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>

1. Consider the plane 4x+y-2z=4 and
the line r(t) = < t, -2t,
-tt >.
a. find the unit normal vector N of the plane.
b. as a function of t find the distance between
r(t) and the plane.
2. Consider a fruit fly flying a room with velocity
v(t) = < -sin(t), cos(t), 1 >
a. if the z = 1 + 2(pi) is the room's ceiling, where
will the fly hit the ceiling?
b. if the temperature in...

(a) Find the distance between the skew lines l1 and l2 given
with the vector equations l1 : r1(t) = (1+t)i+ (1+6t)j+ (2t)k; l2 :
r2(s) = (1+2s)i+ (5+15s)j+ (−2+6s)k.
(b) Determine if the plane given by the Cartesian equation −x +
2z = 0 and the line given by the parametric equations x = 5 + 8t, y
= 2 − t, z = 10 + 4t are orthogonal, parallel, or neither.

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