2. ( eMsa lan--a22 3. All 2-tuples representing points in the first quadrant of the plane including the origin.

Q: b) Show that the points A = (1, 2, 2), B = (3,4, 5) and C = (-1,0, –1) lie on a plane through the…

A:

Q: 10. Suppose that II1 and II2 are parallel planes in R’, given by: Il : ajx + bịy + C1z = di, and II2…

A: Given two plane which are parallel  Π1:a1x+b1y+c1z-d1,  Π2:a2x+b2y+c2z-d2 and another plane is…

Q: What is the point of intersection of the following line and plane: line: 7 = [3, 1, 2] + t [1, - 4,…

A: Given  r⇀=3,1,2+t1,-4,-8& plane π=4x+2y-z-8=0 To find point of intersection:

Q: Considering only the 4-point planes that are drawn in the figure below, which point does NOT share a…

A:

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

A: Solve the given

Q: 4- Find The cquation ofthe plane That pass hrangh the origin audat the poiat p(11)ond at is parallel…

A: To find the equation of plane passing through the origin, the point (1,1,1) and parallel to the line…

Q: 9. Give a geometrical interpretation of the intersection of the planes with equations x+y-3=0…

A: Give a geometrical interpretation of the intersection of the planes with equation. x+y-3=0 y+z+5=0…

Q: Find a parametric representation of the line through the points P(4,1,2) and Q(3,5,7)

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Q: 1 2x 3y + z = 0 and 2 +t - 1 1

A:

Q: 2) Calculate the distonce d of the pint ? (-l,(, -2) from the plane passing through the three A(…

A:

Q: 4 Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0, z+x3=0,…

A: Find the four vertices of the tetrahedron.  Making four equation.  Then write it in matrix form.…

Q: (42) is the distance between the point (1, –3, –2) and the plane x- 4y-3z-2= 0.

A: In this question we have to find the distance between point and plane. Note: As per our policy we…

Q: 4- Find The equation ofthe plane That the origin andat the poiat p(u1)ond at is parallel to theline…

A: Equation of plane

Q: If the plane r contains the points P(1, 0, 0), Q(3, 2, 0), R(0, 2, 1), W(a, 1, ), then a = O 1 -6 O…

A: We Find the equation of plane passing through P,Q,R and then substitute the point W in the Plane…

Q: show that the points AC!,l,4) B(2,2,2), coplanear (in the c(o,l,5) and D (1,0,5) are Same plane).

A:

Q: ind a plane containing the point Gl,2,-3) and the line of intersection of the pladnes -X+3y -Z E -7…

A:

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: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

A:

Q: 0- Draw a sketch of the Plane of 4x-tyt22-9=0

A: Solution

Q: A __________ is the set of all points in a plane that are equidistant from a fixed line (called the…

A:

Q: A. Use the figure on the right to name each of the following: 1. three collinear points 2. three…

A: A) 1) Collinear points are the points which are on the same line. Hence 3 collinear points are A , P…

Q: ---- Let a, = |4|, a, = 3 and let b = |1, for what value of h is b in the plane spanned by a, and…

A: Given that a1=145,  a2=238   and  b=11h. This implies that, xa1+ya2=bx145+y238=11hx+2y=1…

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: 23. Through (1,3, 5) and normal to7 - } +k.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. Which of the following figures is not a rhombus?

A:

Q: In the Argand's plane what is the locus of [3(22²-5z + 3) 11_2π ong

A:

Q: Find an cqu of fangat plane the to the gapu xー4y+ プい16

A: Let f(x, y, z) = x2 - 4y2 + z2 - 16 . Let (a, b, c) be a point lies on the given surface.  That is…

Q: 7x + 3y + 4z = 5, and 21x + 9y +12z = 13

A:

Q: Find the equation of the plane that contains point P(1, -1, 2) and has the normol n= 2¿+3j+Sk.

A:

Q: Find the equation of the plane which passes through O and is parallel (5а + бу) — 3 to z – %3D

A: The equation of given plane is,      z - (5x + 6y) = 3⇒ z - 5x - 6y = d   for a plane of the form ax…

Q: 5. What can you change to the two planes to make them parallel? Make as few changes as possible and…

A: given planes π5: 2x-4y+2z-2=0π6: x-y+3z-2=0

Q: 10. The distance between the point (3,-2,5) and the plane 2x+2y+z=5 is NONE

A: Given: The distance between (3,-2,5) and the plane 2x+2y+z=5

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: Зх + 2у + 3z %3D 6

A: Use a graphing utility to plot the graph of 3x+2y+3z=6 .

Q: Зу — 2z 3D 6

A: Use a graphing utility to plot the plane, 3y-2z=6 .

Q: 2. Use analytic geometry to verify that quadrilateral JKLM is a parallelogran 1C). YA K(-1,1) 2 -2 0…

A:

Q: 3 2. Dilation of - for AABC AJVL about the origin, 3. 2. then (x, y) (x - 0.5, y + 4.5)2. C. ДАВС.…

A:

Q: 1 Identify the statement as true or false and justify your answer. If m is perpendicular to plane T…

A:

Q: You are given the following points: A = (-4, 20, 16), B = (20, 0, 7), C = (8, –15, – 19). %3D Which…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Evaluate ||x'y dA if D is the triangle in the xy-plane with vertices at (0,0), (5,2), and (0,2).

A:

Q: In the study of plane geometry, certain basic statements called axioms or postulates are accepted as…

A: To check if the statement is true or false

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

A: The given problem can be proved both by mathematically and by the definition. For your convenience I…

Q: If a? + b² + c² =1, then the distance from P (x0, y0, z0) to the plane ax + by + cz = 0 is |. |.…

A:

Q: 1. Find the plane through the points A(1,2,-), B(4,2,-2) and 4' C(2,3,4)?

A:

Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…

Q: If A, B, C, and D are collinear, then they lie in the same plane. A, B, C, and D lie in the same…

A:

Q: Given four points A(2, 3, 5), B(6,9, 15), C(0,0, 5), D(-2, –3, 10) in 3D Cartesian coordinates, we…

A: We are given four points on the 3D Cartesian coordinates with the image plane as z=2 And we have to…

Q: tor that is norma to the Plane determined by the three Points i+ 2j +k, si-j+ k , 3i + 2; - 7k.

A:

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

A:

Q: Consider the points P = (3, 2, 1) and Q = (1, 2, 3) in R3. (1) What is the equation of the sphere…

A: Answer

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.