be Sreal number. Explain why the planes a X + 2y + az = 1 and ax + 2y + az = 17 are not osethogonal

Q: Determine the Miller indices of a plane that makes intercepts of (4, 3 and 8) on the coordinate axes…

A:

Q: Calculate gij for the distance between (x;) = (1, 1, – 1) and (yi) = (0,1,2) in %3D T-2 1] barred…

A: A point in three dimensional coordinate system is given by xi=1,1,-1yi=0,1,2 Now the point in barred…

Q: Describe a method for determining whether four points P, Q , R , and S lie in the same plane?

A: We will show a method for determining whether four points P,Q,R and S lie in the same plane.

Q: Find a parametrization for the line segment beginning at P,(4, - 7,- 7) and ending at P2(0, - 7,2).

A: The line segment beginning at P1<4, -7, -7> and ending at P2<0, -7, 2>

Q: 1. Get center point of homo geneu us plane limited by 9) y =4- x2 and x axis

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

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: prove that the three planes 2x+y+z = 3 , x-y+2z = 4, x+z = 2 from a triangular prism and find the…

A:

Q: Find the distance (in appropriate units) between the points P(2,−1)P(2,−1)and Q(3,4)Q(3,4)in the…

A:

Q: Suppose that (a) point C lies in plane X and (b) point D lies in plane X. What can you conclude…

A: Let point C and D lies in plane X. A straight line can be formed by joining the points C and D. Let…

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: 2. Let D be the parallelogram in R? whose vertices are (0,0), (1, 1), (2, –1) and (3,0). By substi-…

A: We have to the value of integral.

Q: where P is the parallelogram Spanned by the Vectons 24,13 and <3,3) with tHanformation X=4u+3V and.

A: Given that ∫∫Pe4x-ydxdy where p is the parallelogram spanned by the vectors 4,1 and 3,3 with…

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

A:

Q: If the coordinates of the mid-points of the sides of a triangle are (1,1) ,(2,-3) and (3,4) .Find…

A:

Q: The distance from (4,-5, 10) to yZ-plane is O A.4 O B. 5 C. /141 OD.10 OE. 125

A: Solution is given below:

Q: Use Clairaut's theorem to draw the geodesics of the catenoid

A: Solution :-

Q: Show that the distance between the two points z1 and z2 in anArgand diagram is | z1 - z2 | .

A: Argand diagram:  1 It is a plot of complex numbers as point.  2In the complex plane using…

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

A:

Q: Let S be a set of five distinct points in the plane with integer coordinates. Show that the midpoint…

A: Given S to be set of five distinct points in the plane with integer coordinates. Let the coordinates…

Q: Prove that the points 3,0),(4, 5),(-1, 4) and (-2,-1) taken in order, Lorm a rhombus, also find its…

A:

Q: Prove that a projective plane (P,L,I) has the property that every line contains at least three…

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: A computer software exists so that the cursor of the program and ends at the origin of the plane. A…

A: To determine the distance traveled by the cursor.

Q: Draw the image of quadrilateral ABCD under the translation (z, y)-(-7,y+1).

A: from the diagram coordinate of quadrilateral ABCD   is   A(6,-5)    B(0,-3)     C(5,-2)   and (5,-4)

Q: Suppose that point C lies in plane X and point D lies in plane X. What can you conclude regarding…

A: What can you conclude regarding CD↔.

Q: Use Green's theorem to calculate where C is the rectangle with vertices (0, 0), (2, 0), (2, 3), (0,…

A:

Q: Find the general quation of plane containing the point P(-1,3,3), and perpendicular to the line…

A:

Q: Зу — 2z 3D 6

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

Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

Q: A quadrilateral has the following vertices given:  P1 (1, 4), P2 (3, 4), P3 (3, 6), P4 (1, 6).  The…

A: Given points are :  P1(1,4) , P2(3,4) , P3(3,6) , P4(1,6). We will first plot those points in a…

Q: Hiwed Find equations for_thefallawing lines - The line through (3, Sz=2) Perfendiculor toX-z plane

A:

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

A: Form the three vectors and take the determinant of them. If determinant equal to zero it means all…

Q: A cube of cheese from Italy with edge measure of 1 was cut by Mickey using a plane in a manner that…

A: Let us assume the the cordinates OA= OB= OC= 1

Q: Consider the integer points on the xy-plane. How many paths are there from (0,0) to (4,-2)? Only…

A: Consider the integer points on the XY plane. To find paths from (0,0) to (4,-2). Here only down and…

Q: Find the distance from Po = (3, 9, 6) to the plane 3x + 4y – 5 = 0.

A: The given equation of plane is 3x+4y-5=0 and the point is P0=3, 9, 6. The distance between a point…

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

A: We are given the points : A(1,2,14) , B(4,2-2) and C( 2,3,4) Equation of a plane passing through…

Q: Does the plane x = 5 have a trace in the yz-plane? Explain.

A: Given: The plane is: x=5 We have to determine the given plane is trace in the yz-plane and explain

Q: Usually there will be exactly one hyperplane in Rn that contains the n given points x = 0, a1, ... ,…

A:

Q: Which of the following point is the projection of the point (0, 4, 2) on the yz-plane?

A: In this question we have to find the projection of the point on the yz-plane.

Q: Show that the set of all points P, that are twice as far from (-1,5,3) as from (6,2,-2) is a sphere.…

A: Let's find.

Q: Describe a method for determining whether four points P , Q , R , and S , lie in the same plane

A: We know that if some points lie on the same plane, then their slope would be same.

Q: Use Green's Theorem to evaluate $4x²ydx+2ydy where C is the triangle with vertices (0,0), (1,2), and…

A:

Q: Pind all point on 2=8-3x°- 243 where ohe bonyent plane is orehogonal :2-36,リ=タ +&e, 2-5-ビ to the…

A:

Q: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…

Q: calculate Sry³ dA where Ris the vertex of the triangle (0, 2), (1,1) and (3,3 )|

A: The sketch of R is

Q: The distance from (10,-9,5) to yZ-plane is - 10 B.9 OC.5 OD. 206 OE. /106

A: We will find the distance between the point and the yz plane as following.

Q: Find the distance from the point to the plane. (6, 0, —6), т — у %3D 4

A:

Q: Let ABCD be a parallelogram in the affine plane. Prove that the line connecting the midpoints of two…

A:

Q: Show that the two planer diagram represent the homeomorphic surfaces

A: Given:-                 Show that the two planer diagram represent the homeomorphic surfaces

Q: What are the projections of the point (3,−2,−7)(3,−2,−7) on the coordinate planes? on the xy plane?…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.