2. The plane goes through point A(1,–2,3) and is parallel to the lines x = 2t y = -t +1. Write plane equation. z = 3 х-2 y+2 z+1 and 2

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: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

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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: (b) Find an equation of the plane that contains the line x = 1 + t, y = 2-t, z = 4 - 3t and is…

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Q: Find an equation for the plane that contains the line v = (-1, 1, 2) + t(9, 5, 4) and is…

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Q: If Ax+By+5z=C is an equation for the plane containing the point (0,0,1) and the line x-1=2, z=-63,…

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Q: The equation of the plane passing through the point (0, 0, 4) and perpendicular to 4 is: the line 4…

A: Equation of plane

Q: The equation of the plane that contains the three points (1, 2, 0), (1, 3, 1), and (3, 0, 4) is 6x…

A: Cartesian equation of a plane passing through three non collinear points A(x1,y1,z1), B(x2,y2,z2),…

Q: Find an equation of a plane containing the line r = (4, –5, –4) + t (–7, 8, –4) which is parallel to…

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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: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

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Q: 1. Find an equation of the plane that contains the line r = -2+ 3t, y = 4+2t, z = 3 - t and is…

A: We have to find

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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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: 16.) Which of the following lines is parallel to the plane? 2x- y – 4z = 4 (a) x=2+1, y =-2-2t,…

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Q: The line : X - 3t, y = 1 - 2t, z = 2 - t is perpendicular to the plane: X - y - z = 1.[g]

A: Given that equation of line x=-3t ,y=1-2t ,z=2-t and equation of plane x-y-z=1To chaque the line and…

Q: 3. Find the general form of the equation of the plane containing the point Q(0, -2, 10) and the line…

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Q: 1 2x 3y + z = 0 and 2 +t - 1 1

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Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: The equation of the plane passing through the point A(6, 6, 6) and orthogonal to the line a = 11 +…

A: The objective is to find the equation of the plane passing through the point A6,6,6 and orthogonal…

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: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: 15. Find an equation of the plane through the point (-2, 4, 6) and perpendicular to the line r = t,…

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Q: 4. Give the general equation of the plane containing the point (3,-1,4) and 2- z perpendicular to…

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Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

Q: 10) Find the point of intersection of the lines L4:x = 1+ 2t, y = 2 + 3t, z = 3 + 4t and L2: x = 2 +…

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Q: 3. Find the distance from P(1, 1, 1) to the plane II with equation r – 3y + 4z = 10.

A: Distance between point and plane is (4√26)/13.

Q: 6. Find the intersection of the line I and the plane r. 1:F = (4,-1,4) + t(5,-2,3) T: 2x+5y+z+2=0

A: answer is in next step

Q: 1. Find an equation for the plane through P,(0,2,–1) perpendicular to n = 3i – 2j-k

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

Q: 2. Find an equation of the plane that contains the line r = 1 +t, y = 2 - t, z = 4 – 3t, and is…

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Q: find the equation of the plane with the given description. Passes through O and is parallel to 4x −…

A: Solution:Given    A plane 4x − 9y + z = 3To find the equation of the plane passess through O and is…

Q: Find the equation for the plane through Po(4,9,-7) perpendicular to the following line. x-4+t,…

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Q: Q1) the plane has equation of 4x-3y-2+5=0 Pud equation of plane partlel to R) and contimons with…

A: Given that: Equation of given plane is: 4x-3y-245=0and contains point (2,1,3)

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: Find the general form of the equation of the plane containing the point Q(0, –2, 10) and the lin l1…

A: Let's find.

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: 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: Determine the point at which the line passing through the points P(1, 0, 6) and Q(7, -1, 7)…

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Q: If Ax+By+5z=C is an equation for the plane containing the point (0,0,1) and the line X-1=と+2 3…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: Here, the given equation of the plane is: 4x+7y=10...(1) And the given equation of the line is:…

Q: 6) = Find the point at which the line intersects the given plane. x =3 - t, y = 2 + t, z = 5t; x - y…

A: Equation of a Line in Parametric Form: where are functions of and is the parameter The equation of…

Q: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

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Q: Find the equation of the plane through P(2, – 1,1) that is parallel to Il: 2x + 3y + z – 12 = 0. %3D

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Q: Find an equation of a plane containing the line r=⟨0,−5,−1⟩+t⟨−2,4,−2⟩ which is parallel to the…

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Q: Find the point at which the line intersects the given plane. x = 4 - t, y = 5 + t, z = 3t; x - y +…

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Q: 9. Determine the Cartesian equation of the plane that contains the intersecting lines: -2 y 2+3 x-2…

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Q: Find the equation of the plane that contains the point P(3,5, –1) and the line = 4 – t, y = –1+ 2t,…

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Q: The equation of the plane passing through the point A(4, 9, 4) and orthogonal to the line a = 9 +…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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