3. If a plane contains two distinct points Pi and P2 then show that it contains every point on the line through P and P2

Q: Given W(-1,5,2), X(6,-2,3) and Y(-2,-7,-3), are points in 3D, then determine the area of…

A: To find the area of the parallelogram formed by two vectors

Q: The set of all points in a plane that are equidistant from a fixed point is a/an is called the The…

A: To Fill up the blanks: The set of all points in a plane that are equidistant from a fixed point is…

Q: 1. Let A, B, C, and D be four distinct points in the plane. Suppose that no three of them lie on a…

A:

Q: Show that three points P , Q, R are collinear (lie on a line)if and only if −→P Q × −→P R = 0.

A: Given: Show that three points P, Q, and R are collinear (lie on a line) if and only if PQ→×PR→=0

Q: If there were no understood restriction to lines in a plane in Theorem 1.4.3, the theorem would be…

A: The given statement is " In space, there is exactly one line perpendicular to a given line at any…

Q: Prove the converse to theorem 2.6.2 let l and m be  two lines. If there exists a unique point P…

A: Solution:→                  Let Assume;                        Lines are not distinct.…

Q: In the three-dimensional space, consider a cube Q and a plane P passing through 4 vertices of the…

A:

Q: 6. Show that the diagonals of the square with the given vertices are congruent perpendicular…

A: The formula for the midpoints of (x1,y1) and (x2,y2) is x2+x12,  y2+y12 and the formula for the…

Q: # 7. If we invent the line at infinity in the projective plane, then it is possible to construct one…

A: Given that if we invent the line at infinity in the projective plane,then it is possible to…

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: ( , s) Let A = (-1,3) and B = (2, 4). Find the set of points C such that the area of triangle ABC is…

A:

Q: 16. Consider the points P(1, 2), Q(-2,1) and R(1,0) in the plane. Which one of the following…

A: 3 points are in the plane Which Statment is true ?

Q: In the following problems, L is a line, E is a plane containing L, and H1 and H2 are the half-planes…

A: Since, you have post multiple part here. I am answering first one. Please post again for remaining…

Q: Let A and B be points in the plane and consider the ray AB, show that if l is a line that passe by A…

A: Let A and B be the points in the plane and consider the ray AB→. Given that l is a line that passes…

Q: If m, n, and t are distinct lines in the same plane such that mIt and t In, then m n. O True O False

A:

Q: Prove a quadrilateral with vertices G(1,1), H(5,3), I(4,5) and J(0,3) is a rectangle

A:

Q: 6. Find a plane with the P (3, – 4, 5) and contains the line L:= =*

A: It is given that plane passes through (3,-4,5) and the DR's of a given line is 2,-3,5.

Q: Find the plane through P = (4, −1, 9) containing the line r(t) =〈1, 4, −3〉+ t〈2, 1, 1〉.

A: The plane contains the line r(t)=1, 4, -3+ t2, 1, 1, so a vector in the plane is 2, 1, 1. The line…

Q: Given that all three points (6, 10, 10), (11, 14, 13), and (k, 8, 6) lie on a plane that contains…

A: If three points lie on the same plane then determinate of matrix made by that points is zero.…

Q: 1. How can two pencils (representing lines) be held so that a plane can be passed containing both;…

A: Please submit parts 2 and 3 separately for them to be answered. For the first part, Two lines, in…

Q: 9. Suppose z1, z2, z3 are the vertices of an equilateral triangle inscribed in the circle |z| = 2.…

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Q: Prove that C is on the perpendicular bisector of segment AB.

A: Solution:Given A(-4,-3), B(6,1) and C (5,-11)To Prove: C is perpendicular bisector of ABi.e., to…

Q: Find an eguaton for the set of all points (a sy, z) equiditant fom point (1,0,2) and

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Q: 34) Show there is no plane perpendicular to n= î +î that passes through points P(1, 2, 3) and Q(2,3,…

A: Since you have submitted multiple question, we will solve the first question for you. To get the…

Q: The set of all points in a plane that are equidistant from a fixed line and a fixed point is a/an…

A: Parabola is defined as a curve made up of all points that are equidistant from a fixed line and a…

Q: 9. Suppose z1, z2, Zz are the vertices of an equilateral triangle inscribed in the circle |z| = 2.…

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Q: (b) Let A(4,4, 7) and B(11,8, 11) be two points in 3D. Determine the coordinates of the point Q…

A: Introduction: When a vector is a non-zero scalar multiple of another vector, the two vectors are…

Q: For every two lines intersecting in space, there is only one plane in them True false

A:

Q: prove Theorem 4P.1 Theorem 4P.1 There are exactly six lines in the four-point geometry.

A: The known fact is that in four point geometry, any two distinct points have exactly one line on both…

Q: Let points A, B, C, and D in R3 have respective coordi- nates (1, 2, 3), (−2, 3, 5), (0, 3, 6), and…

A: A1, 2, 3, B-2, 3, 5, C0, 3, 6  &  D3, 2, 4. Now,…

Q: with the guldin's proposition 1 get the contents of the rotating object that occurs if the land…

A: As per the question we are given a 2d region bounded by the curve : y = 6 - 3x - x2 and the straight…

Q: 10 11 3 vertices at a parallelograni AaCD are shown in the appiet What are the coordinates of point…

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Q: Suppose that four lines in a given plane a1, a2, b1. bz are given, with the conditions (also given)…

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Q: Find the coordinates of point P along the directed line segment AB so that the ratio of AP to PB is…

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Q: 1. Do the planes x1+x2+x3 = 1, x1+x2 = common point of intersection? If they do, find such a point.…

A:

Q: Consider the following geometry problems in 3-space Enter T or F depending on whether the statement…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: 1) which of the following pairs of planes cross along a straight line a) x+2y-3z-4=0…

A: General Equation of Plane: The general equation of the plane is given by where are constants Line:…

Q: Let A, B, C be three collinear points and let P be a point outside the line through A, B, C. Using…

A: Sketch the diagrams with the help of geometrical tools and the hint given in the question.

Q: Solve the following problems completely. If there are seven distinct points on a plane with no…

A: Given: Total number of points is, n=7. No three points are collinear. The objective is to find the…

Q: If there are 7 distinct points on a plane with no three of which are collinear, how many different…

A: A polygon is a closed shape in two dimensional. It do not contain any curves. Thus the minimum…

Q: Which of the following statement is FALSE? The intersection of two planes is either a point or a…

A: Statement 1 is false . The intersection of two planes is always a line .  Since Planes are infinite…

Q: Prove that if P(I, y) be any point on the line segment joining R(11, Y1) and P2(12, Y2) then I= I1+…

A: Let P divides P1 and P2 in the ratio k : (1-k) x=kx2+1-kx1k+1-kx=kx2+x1-kx1x=x1+kx2-x1 Similarly…

Q: 1. Find the plane which contains the point M (4, 5,0) and the line 2+3 = ¹ = 2²

A: To find the plane which contains the point M4, 5, 0 and the line x+35=y-4-3=z-22.

Q: 1-) Determine the values of a ond b which the planes 2x -y+ 32-1=0, x+2y-2+b = 0, X+ay-6 2 +10 = 0…

A: Here, we have three planes: Plane I: 2x-y+3z-1=0; Plane II: x+2y-z+b=0; Plane III: x+ay-6z+10=0.…

Q: What are the coordinates of the point on the directed line segment from (-7, 10) to (-2, -5) that…

A: Given points is : -7,10 and -2,-5 m:n=2:3, thereforem=2n=3 -7,10x1=-7y1=10-2,-5x2=-2y2=-5

Q: Show that the points E(2, 2, 2), F(2, 0, 1), G(4, 1, -1) and H(4, 3, 0) are coplanar and that they…

A:

Q: 3. If a plane contains two distinct points P1 and P2 then show that it contains every point on the…

A:

Q: 3. Draw and describe the locus of points in the plane that are equidistant from the endpoints of DE.

A: Step:-1 According to a known result "The locus of Points in the plane is perpendicular bisector of…