Suppose we know that the points P (0, -1, -1), Q(1, 1, 4), and R (2, -4, 0) form a triangle in 3-space. We want the standard form of the plane that contains that triangle. Evaluate PQ and PR. Write down the standard form of the plane that contains that triangle. (???)(x-???)+ (???) (y-???) + (???)(~-???)= 0

Q: Find the requested equations below Find some symmetric equations for the line formed by the…

A:

Q: 1. Find an equation of the plane that passes through the points (-1, 3, -3), (4, 1, 2), and (8, 2,…

A:

Q: .Find the equation and sketch the plane that contains the points (2, 6, 1), (-4, 9, -1) and (4, 3,…

A: Equation of plane is 3x+2y+6z = 12

Q: In the projective plane, Z5P2, find the line that contains the points (1,2,1) and (2,1,4).

A: In projective geometry over a finite field, such as , we can find the line that contains two points…

Q: etermine the intersection point of the two lines or show that they do not intersect. a. Does the…

A: Given: (-5,4,-1) and (-3,-5,0)

Q: O(0,0) and A(4,4) are two given points and B is any point. Find the equation to the locus of the…

A: Given The O(0,0)  and  A(4,4) are any two points and  B is any points . OB and AB are perpendicular…

Q: For each pair, determine if the planes are parallel, orthogonal, or neither. Explain your answer.…

A: The normal vector of a plane is a vector that is perpendicular to the plane. It can be found by…

Q: Find the equation of the plane parallel to the line r = 2i + t(−4i + 3j + 8k) and containing the…

A:

Q: Q4-Find the Cartesian equation of the line that passes through the point (-3, 2,-1) and is parallel…

A:

Q: 7. Let z = -3 + 5i. Plot the points z,-z,7,-ž and - in the complex plane.

A:

Q: Plot the following sets of points in a Cartesian plan given set of points consecutively to form a…

A:

Q: What are the projections of the point (−2, 3, 4) on the xy-, xz-, and yz-planes? Draw a picture and…

A: Given, the point (-2, 3, 4), we have to find the projections of this point on the xy-, yz-, and…

Q: Find an equation of the plane passing through the three points given P = (2,4, 2), Q = (4, 10, 10),…

A:

Q: Let A:(-1, 1, –1), B:(2,0, 2), C:(4, 1, –3), and D:(-3, 1, 10) be points in R. (a) Find the angles…

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

Q: Eindequatisf ihe line passer thronghthe Paint (-3,2,-)-and parallelte the lineof intersaction of the…

A:

Q: Another constraint you can use to compute cubic splines is that the second derivatives of adjoining…

A: Consider the cubic polynomial  fx=⋮ai-1x3+bi-1x2+ci-1x+di-1, x∈(xi-1,xi]aix3+bix2+cix+di…

Q: You are given the following points: A=(−4,20,16)A=(−4,20,16), B=(20,0,7)B=(20,0,7),…

A: Given- (x,y,z) coordinates of three points :A =(-4,20,16) B=(20,0,7) C=(8,-15,-19) to find- closest…

Q: The paths of four insects crawling up the side of a building are shown in the Cartesian plane below.…

A: