Question

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

Answer #1

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...

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

Consider the lines in space whose parametric equations are as
follows
line #1 x=2+3t, y=3-t, z=2t
line #2 x=6-4s, y=2+s, z=s-1
a Find the point where the lines intersect.
b Compute the angle formed between the two lines.
c Compute the equation for the plane that contains these two
lines

show that L: x=1-2t .y=t .z=-t
and the plane P: 6x-3y+3z=1
are parpeudicular then find the point of intersect

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

Consider the line L with parametric equations x = 5t − 2, y = −t
+ 4, z= 2t + 5. Consider the plane P given by the equation
x+3y−z=6.
(a) Explain why the line L is parallel to P
b) Find the distance from L to P .

Decide whether the given line and plane intersect or not. If
yes, find the point of intersection.
plane : 4x−5y+2z=−34x−5y+2z=−3
line : <−2t,−1+3t,2+4t>

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

Consider the plane x + 2y + z = 2 and the point P = (2,0,4) A)
Set up an equation to measure the distance d from P to an arbitrary
point (x,y,z) on the plane B) Find the pointe on the plane that is
closest to P C) What is the shortest distance between point P and
the plane?

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

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