13. Find an equation for the plane passing through the points P = (5, 1, 1), Q = (-1, 1, –2), and R= (2, 0,3). %3D

Q: 11) Find the equation of the plane that passes through the point (1, 5, 1) and is perpendicular to…

A: A plane is passing through a point (1,5,1) and is perpendicular to the planes 2x + y - 2z = 2 and x+…

Q: Find the equation of the plane with the given description. Passes through (6, 1, 5) and is parallel…

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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. Determine the equation of the plane that contains the point (0,3,0) and the X = 1 line y = 2t z =…

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Q: Find an equation for the plane in R³ spanned by the points (1,5,

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Q: 4] Find the equation of the plane that contains the point (a, 0, 0), (0, b, 0) and (0, 0, c).

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Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x= -6+t, y…

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Q: Find the point at which the line (3, 4, 5) +t(1, -1, –5) intersects the plane -5x + 2y+ z = -86.

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Q: Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and passing…

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Q: Find the equation of the plane that passes through the points 4 = (2,4,-3), B = (3,-1,3) and y - 4 -…

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Q: Find an equation of the plane passing through the three points given.P = (2, −1, 4), Q = (1, 1, 1),…

A: To find the equation of the plane passing through the three pointsP =x1,y1,z1= (2, −1, 4), Q…

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: 6. Find the equation of the plane that passes through (3,1,2) and (-1,2,–1) and is parallel to the…

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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: find the equation of the plane through P(1, 3, 2) that is parallel to the plane 5x - 4y + 3z = 7

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Q: Find an equation of the plane passing through the three points give P = (4, –1, 2), Q = (1, 1, 1), R…

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Q: Find the Cartesian equation of the plane through the point (5, 1,0) and parallel to the lines = 2+t,…

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Q: Find an equation for the plane through P(1,4, 4) that contains the line of intersection of the…

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Q: equation

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Q: Find the equation of a plane through the point (1, – 1, 6) and orthogonal to the line x(t) = 7 + 4t…

A: Required plane is orthogonal to the given line, say L: x(t)=7+4ty(t)=-3-4tz(t)=-1-6t also, the plane…

Q: (11) Find the equation of the plane through points P(5, –2, – 14), Q(-3, –4, 20), R(-1, –2,4).

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Q: O Find equations of the line that passes through the point (2,0,3) and is normal to the plane x – 2y…

A: We will find out the required equation of line.

Q: 3) Let r1(t) = and r2(t) = be two skew lines. Find the equation of the plane which lies exactly…

A: Given r1(t)→=t,t+2,2t and r2(t)→=t+1,2t+1,t+1 are two skew lines. We have to find the equation of…

Q: Find the general form of the equation of the plane with the given characteristics. Passes through…

A: The plane, let P1, whose equation is required is perpendicular to the plane, And passes through the…

Q: Find an equation of the plane containing the points P(O,0,o) and Q(2,2,2) and parallel the line…

A: Given:- Equation of line x= t, y = 1,z= t  To find:- An equation of the plane containing the points…

Q: Find the equation of a plane that passes through the point (0,0,0) and contains the line x = 2 -t y…

A: Here we have to find the equation of a plane that passes through the point (0,0,0) and contains the…

Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

A: Plane and line

Q: Determine the equation of the plane through the points (1, 0, 3) and the line l : ¯r = (3, 4, 1) +…

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Q: 25. Find an equation of the plane through the line of intersection of the planes x – z = 1 and y +…

A: Equation of a plane P that passes through the line of intersection of two planes P1 and P2 is given…

Q: 12) Find the intersection of the plane: x – z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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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: The equation of the plane through P.(2, 4, :5) perpendicular to the line :X = 5 +t ,Y= 1+ 3t , Z= 4t…

A: (.)  Let the point Px1,y1,z1 and perpendicular line  x-x0a=y-y0b=z-z0c Then the equation of the…

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: 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 the equation of the plane that contains both of the lines given below. Line 1: x = 1+t, y = 2+…

A: Line 1 : x=1+t, y=2+2t, z=3-t        ⇒a⇀=1, 2, 3, l⇀=1, 2, -1 Line 2 : x=1-s, y=2+4s, z=3+2s…

Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

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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).

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Q: 3) Let r1(t) = and_r2(t) = be two skew lines. Find the equation of the plane which lies exactly…

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Q: Find the equation of the plane through the points P (1,-1, 1) Q = (3,–1,3); R= (2,1,1).

A: We will find out the required equation of plane.

Q: 2. Find the coordinates of the y-intercept of the plane (x, y, z)=(4,6,5) +s(2,3,1) + t(3,6,12)

A: To find out the coordinate of y-intercept.

Q: 5. Find the equation of the plane that passes through the point (6,0,-2) and contains the line X =…

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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: Determine the general form of the equation of the plane passing through P(2,1,-1), Q(0,-2,0) and…

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Q: A normal equation of the plane that contains the line 1₁: (x, y, z) = (1, -1, 2) + t (9, 1, 3), t E…

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Q: Find the general equation of the plane passing through P(−1, 3, −2) and having n = (−2, 1, −1) as a…

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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: 4] Find the equation of the plane that contains the point (a, 0, 0), (0, b, 0) and (0,0, c).

A: As per our company guidelines we are supposed to answer only one question kindly post other parts in…

Q: Find an equation for the plane containing the two (parallel) lines v, = (0, 1, –4) + t(1, 3, –5) and…

A: Solution: The objective is to find an equation for the plane containing the two parallel lines

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

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