In Exercises 1–3, give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. 1. x2 + z2 = 4, y = 0 2. x2 + y2 + z2 = 1, x = 0 3. x2 + y2 + z2 = 25, y =-4

Q: In Exercises 21-24, find an equation of the plane passing through the threepoints given.24. P = (2,…

A: we have to find an equation of the plane passing through the given points are P=(2,0,0) , Q…

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

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: In Exercises 47-50, verify that Wy %3D Wex- 47. w In (2x + 3y) 48. w = e + x In y + y Inx

A: NOTE-  As per our guidelines we have to solve only first question. Given data- w = ln ( 2x + 3y ).…

Q: Describe the set of all points P ( x , y ) in a coordinate plane that satisfy the given condition. 8…

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: 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: 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: (a) y= -2 (d) xy = 0

A: Consider the given information.(a)The given condition is y=-2.The line y=-2  is a vertical line,…

Q: Determine the Eq.  of plane (M) pass through points A(0,2,0), B(1,1,1), C(-1,0,2)

A:

Q: graph the points z = x + iy that satisfy the givenconditions.a. | z | = 2 b. | z | < 2 c. | z |…

A: a. We have given z=2 Then, put z=x+iy This implies that x+iy=2x2+y2=2x2+y2=4 Therefore, x2+y2=4…

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: 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: If the plane F contains the points P(1, 0, 0), Q(3, 2, 0), R(0, 2, 1), L O 1 6 -6 O -2

A:

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

A: To describe the geometric curve satisfied by the equation.

Q: In Exercises 1-12, sketch the graph described by the following cylin- drical coordinates in…

A: Since we are given with the multiple number of question and our guideline is solve first question…

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: In Exercises 19 and 20, describe the domain of ƒ in words. 19. (a) f(x, y) = xe-Vy+2 (b) f(x, y, z)…

A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve…

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: In Exercises 5–10, graph the points z = x + iy that satisfy the given conditions. b. z| 2 5. a. z =…

A:

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: 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 23–24, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = 1 + xy2 - 2z2 24. ƒ(x, y, z) = xy + yz…

A:

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

A:

Q: In Exercises 45-50, find the trace of the plane in the given coordinateplane.45. 3x - 9y + 4z = 5,…

A: Given: The plane in the given coordinate plane,  3x-9y+4z=5, yz.

Q: Exercise 3.1.26 Show that the line through two distinct points (x1, yı) and (x2, y2) in the plane…

A: As we know that: The equation of the line passing through the points x1,y1  & x2,y2.…

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

A: x2+y2=4, z=0

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: Section 2.5 in Volume 3 0) 3. Find the distance the point (4, 5, 2) is away from the plane 2a 7y+ z…

A:

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

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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.