In Exercises 1–3, give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. 1. x =-1, z = 0 2. x = 1, y = 0 3. x2 + y2 = 4, z =-2

Q: 5. Write a rule for the translation of a point of the plane figure above. A. (x,y)→ (x-2,y+3) B.…

A: Translation of a point of the plane means moving all the points of that plane to a new coordinate.

Q: Find a parametric representation of the line through the points P(1,-1,2) and Q(3,1,8).

A: The parametric equation of line through the points x1,y1,z1 and x2,y2,z2 is given by  x=x1+tx2,…

Q: 12 3. 5. 13 18 -1 For what value of hs in the plane spanned by j and i? Preview Answers Submit…

A:

Q: Use drawings as needed to answer the given question

A: (a) In Euclidean geometry, if two or more than two points lie on a line close to or far from each…

Q: (6) Let -1 3 1 y = 2 and uj = -1 u2 -1 -2 Find the closest point to y in span{u1,u2}. What is the…

A:

Q: The diagram approximately Illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1= 0 3x+3y+3z+1=0…

A: Given planes are,    x + y + z + 1 = 0  2x + 2y + 2z + 1 = 0  3x + 3y + 3z + 1 = 0    Thus, normals…

Q: In Exercises 1–3, give a geometric description of the set of points in space whose coordinates…

A: Hi there! Thank you for the question, but as per our guidelines we can solve only one question at a…

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A:

Q: give a geometric description of the set of points in space whose coordinates satisfy the given pair…

A: Consider the given equation as x=-1, z=0

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

A:

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: Discussion: 1- Show that Ramp(t) = u(t) dr = t * u(t)

A: The ramp function is very significant function in mathematics. It is the composition of two…

Q: give a geometric description of the set of points in space whose coordinates satisfy the given pair…

A: Given: x2+y2=4z=y

Q: give a geometric description of the set of points in space whose coordinates satisfy the given pair…

A: given,       x2+y2=4and z=0

Q: E. Determine the set of points satisfying the condition described by |z – 2i| + |z + 4i| = 10. Then…

A:

Q: Find an equation of the largest sphere that passes through the point (-1, 1,4) and is such that each…

A: Find the equation of sphere.

Q: In space coordinates system, the y-axis consists of all points of the form O (x, 0, 0) O (0, 0, z) O…

A: we know that(x,y,z) is nothing but distace of a point from origin along the x,y,z-axis

Q: Give a geometric description of the set of points (x, y, z) satisfying the pair of equations z = 0…

A: given: the set of points (x,y,z) satisfying the pair of equations z=0 and x2+y2=1. as we know that…

Q: Let a point a = (2, 4, 5). %3D a) Find the distance from this point to the xy-plane.

A: Consider the point

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

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Q: Describe with a sketch the sets of points 1x, y, z2 satisfying the following equations. y - z = 0

A: First sketch the graph of the function y-z=0 as shown below.

Q: What are the coordinate planes in three-dimensional space? How are they drawn?

A: The Cartesian coordinate system is used to describe three-dimensional space which consists of an…

Q: In Exercises 17-20, find the equation of the plane with the given description.18. Passes through (4,…

A: Solution:-  We have to  find the equation of the plane with the given description.18. Passes through…

Q: The ___________ is the point on a two-dimensionalplane from which the drops originated

A: The ___________ is the point on a two-dimensional plane from which the drops originated.

Q: In Exercises 21-24, find an equation of the plane passing through the threepoints given.21.…

A: Solution:-  an equation of the plane passing through the threepoints given. P=(2,-1,4), Q=(1,1,1),…

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Given that: y2+z2=1, x=0

Q: Give a geometric description of the set points in space whose coordinates satisfy the given pair of…

A: Given  x2+y2+z2=9, z=0 Now transforming the equation we will get x2+y2=9

Q: The diagram approximately illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1=0 3x+3y+3z+1=0…

A: True

Q: In Exercises 17-20, find the equation of the plane with the given description.17. Passes through O…

A: Given, A plane passes through O and is parallel to 4x-9y+z=3

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: Points in space should be given: A(1,1,0)  B(1,2,1)  C(-3,-4,2).  Calculate the coordinates of that…

A: We are given 3 points on a plane π such as A(1,1,0)  B(1,2,1)  C(-3,-4,2).  We need to find out the…

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Consider the set of points in space whose coordinates satisfy the given pairs of equations. x2 + y2…

Q: r = (6,-3,2)+1(2,0,1) + u(1,1,–3)

A: Given point is (0,-1,-8) and the plane is r→=6,-3,2+t2,0,1+u1,1-3

Q: The diagram approximately illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1= 0 2x+2y+2z+2=…

A: We have to solve given problem: Concept:

Q: In Exercises 41-44, find the intersection of the line and the plane.42. 2x + y = 3, r(t) = (2, -1,…

A: Given: To find the intersection of the line and the plane.2 x + y = 3,  r(t) = (2, -1, -1) + t (1,2,…

Q: 10+ 10-8-6 -2 10 4. -4 9- 10 What is the distance between point A and point B on the coordinate…

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Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: y=0, z=0

Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure…

A: Since you have submitted two questions, we\'ll answer the first question. For the second question…

Q: a)Find the equation of the plane in 3- dimensional space passing through the points P = (1, 2, 1), Q…

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

Q: In Exercises 33 and 34, find the distance from the point to the plane.33. (6, 0, -6), x - y = 434.…

A: We have given; 33. (6, 0, -6), x - y = 434. (3, 0, 10), 2x + 3y + z = 2

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Given that, x2+z2=4y=0

Q: Find points in the Euclidean plane corresponding to the points e₁-[3,-5,-1], e2=[1,-2,2], e3 [2,1,0]…

A: By Pn , we denote the projective space of dimension n, defined as follows: Pn=Rn+1 \ {0}~, where '~'…

Q: sketch the given curves together in the appropriate coordinate plane and label each curve with its…

A: "The last equation is considered as y=15x since the given expression does not represent an equation…

Q: Consider AB in the coordinate plane below. 10 7 5 4 3. 2 A B 6 7 89 10 10-9 -8 -7 -6 -5 -4 -3 -2 -1…

A: i am going to solve the given problem by using some simple geometry to get the required result.

Q: In Exercises 41-44, find the intersection of the line and the plane.44. X - Z = 6, r( t) = ( 1, 0,…

A:

Q: Describe geometrically all points P(x, y, z) that satisfy the given condition. X = 1

A: Given the points P(x,y,z) that satisfy the condition x=1.

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.