Any two lines in space are either intersecting or parallel.

Q: 8. Determine whether the lines L,and L2 are parallel, skew or intersecting. If they intersect find…

A: Given data: The expression for the first line is L1: x=3+2t, y=4-t, z=1+3t. The expression for the…

Q: If two planes intersect, then _____.

A: Intersection of two planes is given by,

Q: Determine whether the statement " If two lines L1 and L2 are each parallel to a plane, then L1 and…

A: Two lines  L1 and L2 can be perpendicular to each other and be parallel to the same plane at the…

Q: The distance between the points A = (-3, –2) and B = (3,3) is,

A:

Q: Show that the lines 2 x+3 y-1 and 6 x-12 y-1-0 are not perpendicular

A: As we know that, if the product of slope of two lines are (-1)  then both the both lines are…

Q: The set of all points on one side of a line is called a/an

A: Consider the given statement "The set of all points on one side of a line is called a half-plane".…

Q: Draw all of the lines of symmetry on the shape.

A: The line of the fold is the line of symmetry. Figures or shapes that have exact resemblance to its…

Q: Three points that are all on a line are?

A: Collinear.  If three points lie on the same line, then those three points are said to be collinear.

Q: Determine whether the statement is always, sometimes, or never true. Two lines in parallel planes…

A:

Q: Determine whether the statement " Two lines in space are either intersecting or parallel", is true…

A:

Q: Determine whether the lines are parallel, intersect, or coincide. y=2x+1 and 2x- y=-1 * O Parallel…

A:

Q: If x and x are independent coordinates of a point, show that

A:

Q: Show that the lines whose direction cosines are given by l+m+n=0,2mn+3nl-5lm=0 are perpendicular to…

A:

Q: Show that the lines whose direction cosines are given by 1+m+n=0 ,2mn+3ln- 5lm=0 are perpendicular…

A: The given direction cosines arel+m+n=02mn+3ln-5lm=0

Q: Plot each pair of points and compute the distance between them: (1, 4) and (3, 2)

A: Here given points  x1, y1=1, 4, x2, y2=3, 2 Use the distance formula between two points…

Q: Give the location of Paris as an ordered pair (x, y).

A: As shown in the figure above, Point A lies in the first quadrant, so coordinates will be A(a, b)…

Q: A parallelogram has point symmetry about the point where its two diagonals intersect.

A: Given query is to find that given statement is true or false.

Q: Show that the lines 2 x+3 y-1 and 6 x-12 y-1=0 are not perpendicular

A:

Q: Prove that the point (1,11),(2,15), and (-3,-5) are collinear and find the equation of the straight…

A: Let the given points be A (1,11), B (2,15), and C (-3,-5). Evaluate the slope of the line AB as…

Q: A quantity that has magnitude but no direction is called a/an ------------------

A:

Q: Prove that if two lines are each perpendicular to a third line in the plane, then the two lines are…

A: Let slope of two lines are m1 and m2 and slope of third line is m3 . Now, as both lines are…

Q: Every tow different lines only intersect at one point

A: If a line intersect at more than one point then it coinside

Q: In Cartesian space, the point form of a line is e: (x, y, 2) = (2 + r, -3 + 2r, 5 5r). a) Find the…

A: In cartesian space, the point form of a line is  l : (x, y, z) = (2+r, -3+2r, 5-5r).   a) Find the…

Q: Construct a line parallel to a given line through a given external point. *

A: To draw a line parallel to the given line from the external point v.

Q: In 3 Point Geometry, provide a proof that every line is on exactly two points.

A: To Prove: In 3-point geometry, every line is on exactly two points.

Q: If a line is perpendicular to one of two parallel lines, then it is :_ perpendicular to the other…

A: Let,

Q: The set of all points on one side of a line is called a/an________ .

A: The set of all points on one side of a line is called a/an________ .

Q: ☐ True ☐ False The slope and the intercept uniquely define a line in two-dimensional space.

A: Given the statement regarding slope and intercept in a two dimensional space.  We have to find the…

Q: Consider the following pair of points. (9,−9) and (−5,9) Step 2 of 2: Determine the midpoint of…

A: Consider the provided points, 9,-9  and  -5,9 Determine the midpoint of the line segment joining the…

Q: Assume that all lines that appear tar 1. Find AB

A: We can find the length of AB in the following step

Q: The intersection of the lines x = a and y = b is the point (b, a). true or false

A:

Q: Prove that a line cannot contain three distinct points.

A: We prove that a line cannot contain three distinct points by method of contradiction.

Q: prove that there are exactly two lines parallel to a given line in Pappus' geometry

A:

Q: Two lines that cross at a point are called v lines.

A: Two lines can either cross or run parallel to each other.

Q: Show the line of symmetry of this figure.

A: Line of symmetry is the line which divides the whole figure into two equal parts.

Q: Find the distance between each of the pairs of points.(a) (-1, 5) and (1, -2)(b) (5, 0) and (2, 7)

A: Find the distance between each of the pairs of points.(a) (-1, 5) and (1, -2)(b) (5, 0) and (2, 7)

Q: the length of the line seyment joining the two Pointsof intersection with the two levels of two…

A: For xz level use y=0 and for xy level use z=0.   Then find two point . Then use the distance formula

Q: Is this statement correct?: If two lines are not parallel then they must intersect at a point.…

A: Given:

Q: Explain why a line in hyperbolic geometry must contain two distinct ideal points.

A: We have to answer given Questions.

Q: Show that the lines whose direction cosines are given by 1+m+n=0 ,2mn+3ln-5lm=0 are perpendicular to…

A: Our objective is to show two lines whose direction cosines given are perpendicular.

Q: Which are parallel.

A:

Q: A line is perpendicular to another line, if and only if

A:

Q: Plot each pair of points and compute the distance between them:(a) (1, 4) and (3, 2) (b) (2, 1) and…

A:

Q: Prove that parallel lines determine only one plane.

A:

Q: Consider the two points defined as: (1/2,-3) and (-1/6,- 1/2).The distance between the points is:

A:

Q: Prove that the midpoints of a parallelogram bisect each other using coordinate geometry.

A:

Q: Do two intersecting lines determine a plane?

A: Two lines intersect at only one point.

Q: An angle in a rectangular coordinate system is in standard position if its vertex is at the________…

A: To fill in the given blanks.

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.