6.) Consider the points P(-1,2,5), Q(2, –3, 0) and (i) Write an equation of the plane containing t

Q: Determine an equation for the unique plane that passes through the points P(0,0, 2), Q(0,4, 0), and…

A: Given points are P(0,0,2), Q(0,4,0) and R(8,0,0). Find an equation for the unique plane that passes…

Q: 1. Find the equation of the plane that contains the point (-1, 1, 2) and the line given by x=1-t,…

A: This question is based on 3d geometry.

Q: 5. Find the equation of the plane containing the points P(3, 2, 1), Q(2, 1, -1), and R(-1, 3, 2)

A: Let position vectors of point P(3,2,1) , Q(2,1,-1), and R(-1,3,2) are a→,b→ and c→

Q: Find an equation of the plane that contains all the points that are equidistant from the given…

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Q: (1) Find an equation for the plane that passes through the point (–1,2,2) and contains the line of…

A: Given: Equation of planes x+y-z=5⇒x+y-z-5=0 and 3x-y+5z=3⇒3x-y+5z-3=0 and point -1,2,2, To find: The…

Q: 4. Find the general equation of the plane passes through the points (3,2,1) and (3,1,–5), and is…

A: We have to find the plane equation

Q: (b). Determine the equation of the plane that contains the points P(1, –2,0), Q(3, 1, 4) and R(0, 1,…

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Q: 8. Find the equation of the plane that contains the points P,(3,1,–2), P2(0, –2, 1), and P3(-2, –5,…

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

Q: Find an equation of the plane passing through the three points given.P = (5, 1, 1), Q = (1, 1, 2), R…

A: GivenP=(5,1,1) , Q=(1,1,2) and R=(2,1,1)To find equation of plane passing through the three points.

Q: (24 17. 3417.4) %3D Find the equation of the plane that contains the line x = 3t, y = 6 - t, z = 4…

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Q: Find an equation of the plane containing the three points P(1,2,2), Q(2,-1,4), and R(3,5,-2).

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Q: 1. Find the equation of the plane that contains the following points. (2, –1, 4), (3, 2,0), and…

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Q: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

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Q: Determine the general equation of the plane N passing through the point P(3, –1,2) and parallel to…

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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: 13. Find an equation for the plane passing through the points P = (5, 1, 1), Q = (-1, 1, –2), and R=…

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

A: Solution

Q: Find the equation of the plane with the given description. Passes through P = (3, 5, −9) and is…

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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

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Q: Q1: Formulate the equation of plane in space that contain two points (2,4,-1) and (1,3,-2) and…

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Q: Find the equation of the plane having the points P(1, 2,5), Q(-2, 0, 1), and R(-3,-4,1). 8x + 2y 5z…

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Q: Determine the equation of the plane that contains the points P_0 = (1, 0, 0), P_1 = (0, 1, 0) and…

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Q: Determine the equation of the plane containing the points: P (1, 2, -3), Q (2, 3, 1) and R (0, -2,…

A: Vector equation of a plane passing through three points with position vector P→,Q→,R→is given by…

Q: Find an equation of the plane containing all of the points below: P: (3, -2, -1), Q: (1, 1, 1), R:…

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Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Given: a plane containing the point P(-2, 5, -3) and the line [x, y, z] = [-1,2,5] + s[3, –4,1]…

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Q: 9. Find the equation of the plane through P(1,1,4) that is parallel to the plane x+ 5y – z + 8 = 0

A: The scalar equation of parallel planes differ only by a constant Therefore, equation of the required…

Q: 1. Find the equation of the plane that passes through the points P(2,0,1), Q(1,0,-1) and R(3,0,1).

A: We have, Vectors in the plane are, Therefore, equation of plane passes through 3 points will be,…

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

Q: Find an equation of the plane that contains all the points that are equidistant from the given…

A:

Q: 4. Find an equation for the plane in R spanned by the points (1, 5, 1) and (1,4, 2).

A: Given v1 = (1 , 5 , 1)v2 = (1 , 4 , 2) Let xyz be a point in spanv1 , v2 , so there exist m , n…

Q: Find and describe the intersection of the following line and plane: T:2x+3y-4z =-7 and r = (4,2,5)…

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Q: 2. Find an equation of the plane determined by the points P(1,1,0), Q(1,0,1) and R(0, 1, 1).

A:

Q: Find an equation for the plane containing the three points P = (1, 2, 3), Q = (3, 1, 2), and R = (2,…

A: To find an equation for the plane containing the three points P = (1, 2, 3), Q = (3, 1, 2), and R =…

Q: 8. Determine if point A(-1, -3, 9) lies on the plane T: 8x-3y+2z=4

A: The point lies on the plane if the coordinates of the point satisfy the equation of the plane.

Q: Find an equation for the plane passing through the points Q(2, 1, –1), R(-1, 3, –1), S(3, 1, 0). 1.…

A: We know that equation of a plane is given by ax+by+cz+d=0 As it passes through (2,1,-1), we get…

Q: 1. Find the equations of the planes that are exactly 4 units from the plane 2x-2y+z=6

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Q: 2. Find the eanation of the plane Containing the point (2,3,3)'and the line Of intersÉCtion 'of the…

A: We have to find the equation of plane containing the point (2, 3, 3) and the line of intersection of…

Q: a) Find an equation of the plane passing through the points P=(1,–2,0),Q=(3,1,4) and R = (0, –1,2).

A: Given points are P1,−2,0, Q3,1,4, R0,−1,2. We have to find the equation of the plane passing through…

Q: 5. Find a plane through the points P(1,2, 3), P2(3, 2, 1) and perpendicu- lar to the plane 4x – y+…

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Q: 16- Find the equation of the plane that contains the line = 5 - z, and the %3D point P( 0,5,2).

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Q: Find an equation for the plane in R® spanned by the points (1,5, 1) and (1, 4, 2).

A: We have to find the plane equation for two given points

Q: 3. Find an equation of the plane passing through the points P = (5,1,1), Q = (1,1,2), R = (2,1,1)

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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: a) Find the equation of the plane containing the points P(3, 1, 5), Q(- 1,– 1,– 1), and R(– 2,2, 4).

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Q: 16. Find an equation of the plane through the point (1, 1, –2) and parallel to the plane 3r – z =

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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: 3) Find an equation of the plane which contains the points P(-1,2,1), Q(1, –2, 1) and R(1,1, –1).

A: Equation of a plane passing through 3 points P(x1,y1), Q(x2,y2) and R(x3,y3) is given by,…

Q: 4. Determine the general equation of the plane containing the points P(1, -4, –5), Q(2,0, 13) and R

A: