Question

What is the angle of parallelism for a line l and a point P in the Euclidean plane? Explain why.

Answer #1

Prove (with neutral geometry)
If the angle of parallelism for a point P and a line RS is
Less Than 90 degrees, then there exist At Least Two lines through P
that are parallel to line RS.
Please explain step by step and include a diagram. Thanks so
much!

(Euclidean and Non Euclidean geometry)
Consider the following statements:
Given a line l and a point P not on the line:
There exists at least one line through P which is
perpendicular to l.
There exists at most one line through P which is
perpendicular to l.
There exists exactly one line through P which is
perpendicular to l.
Prove each statement or give a
counter-example E2 (Euclidean Plane), H2 ,
(Hyperbolic Plane)and the sphere S2 (Spherical
Plane)
( Consider...

(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.

a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize
L. Find the point Q where L intersects the xy-plane.
b) Find the angle that the line through (0,-1,1) and (√3,1,4)
makes with a normal vector to the xy-plane.
c) Find the distance from the point (3,1,-2) to the plane
x-2y+z=4.
d) Find a Cartesian equation for the plane containing (1,1,2),
(2,1,1) and (1,2,1)

True or False? (State 'true' or 'false' and add a sentence of
brief explanation.
*An angle is defined as the space between two rays that emanate
from a common point.
*In a Hilbert plane, if line m is parallel to line l, then all
the points on m lie on the same side of l.
*The notion of congruence of two triangles is undefined.
*An incidence geometry must have either the elliptic, or the
Euclidean , or the hyperbolic parallel...

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 .

Consider the point P(1, −1, 0) and the line l : (2, 5, −1) +
t(−1, −2, 1).
(a) Check that P is not on l.
(b) Find the point on l that is closest to P.

Find parametric equations for the line passing through the point
P(4,5,5), intersecting the line <x,
y, z> = <11, -8, 4> + t <3,
-1,1> at a 90 degree angle.

Find the electric field at distance Y at point p above the
straight-line segment of Length L with linear charge density λ.
Point p is located at 1/3 L from the left of the line. Hint: in
this problem you need to find both X and Y components of the
electric field.

Find the electric field at distance Y at point
p above the straight-line segment of length L with
linear charge density λ. Point P is located at 1/3 L from the left
end of the line.
Hint: in this problem you need to find both X and Y
components of the electric field.

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