Q: Area of Plane Region 2. R: y = 6x − x2and y = x2 − 2x.
A: 2). To find the area of the region R: y=6x-x2 and y=x2-2x. Solution: The intersection point of the…
Q: Distance between the two planes: 2.x+3y+4z = 4, 4x+6y+8z=12 ¡s and (A)2 units (B)4 units (C)8 units…
A: The given problem is to find the distance between the given two planes. Given planes 2x+3y+4z=4 and…
Q: Find the plane determined by the intersecting lines. L1 x= - 1 + 3t y =2+4t z=1-t L2 x= 1- 4s y = 1+…
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Q: 5. The line through the point (1, 0; 6) and perpendicular to the plane a + 3y + z = 5 Answer
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Q: Midpoint formula Prove that the midpoint of the line segment joining P(x1. y1- Z,) and Q(x,. Y2, Z,)…
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Q: How do I find the point on a sphere x2 + (y - 3)2 + (z + 5)2 = 4 nearest to a.) the xy-plane b.)…
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Q: 2. Find a plane perpendicular to the planes x + y - 3z = 0 and x - 2y-2z = -1. Your answer
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Q: Plane x+4y-3z=1 is perpendicular to plane -3x +6y+7z D0- O True O False
A: normal vector of plane x+4y-3z=1 is <1,4,-3>and normal vector of plane -3x+6y+7z=0 is…
Q: Tangent of x2/3 + y2/3 + z2/3 = a²/3 surface at any point (Xo , Yo , Zo ) Show that the sum of the…
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Q: 3) Suppose plane P, contains the points A(5,0, –1), B(2,3, 2), and C(-2, 1, –4), and assume P, is…
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Q: A point in space and let's have the line L whose equation is Q(-1,0,1) let 1 L: 3- x = y = 4 4 It…
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Q: a) b) Determine the equation of the line of intersection of planes 1 and 2. Express your answer in…
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Q: find the point (x, y, z) where the line of intersection of the plane a: x-2y + 4z = 0 and the plane…
A: Find the ,line then point on the plane.
Q: Find the distance from the point (5, 5, 5) to the line x = 0, y = 5+ t, z = 5+t. Find the point P…
A: Explanation of the answer is as follows
Q: Two planes x+ y – 27 = 3 and 2x – 3y + z = 1 intersect in a line. a Find the Cartesian equation of…
A: (a) Given that planes are x+y-2z=3 and 2x-3y+z=1 The cartesian equation of the two lines is,…
Q: I3D Find the coordinates of the point (x, y, z) on the plane z = 2 x + 2y + 2 whi X = y =
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Q: Give an equation of the plane determined by the intersecting lines L1 and L2 L1 : x = 2t y = 4 – t z…
A: The equation of two lines is given as follows: L1: x=2t, y=4-t, z=3+t L2: x=2+s, y=-3+2s, z=s The…
Q: 5. Find the point of intersection of the given plane and line. Plane: 2x - y+3z=7 Line: x=-1+t y…
A: We have to find point of intersection .
Q: Tangent of x2/3 + y2/3 + z2/3 = a²/3 surface at any point ( xo ,Yo ,Zo ) Show that the sum of the…
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Q: Area of Plane Region 3. R: x2 + 3y = 4 and x − 2y = 4.
A: Since you have posted multiple questions, as per our policy we will answer first question. Please…
Q: गाण the Simultaneous earvation. ntuy-4 the linel in ay Plane and indiceate the solu tion.
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Q: Tangent of x2/3 + y2/3 + z2/3 = a²/3 surface at any point ( xo , Yo , Zo ) Show that the sum of the…
A: Solution:
Q: 3. Find the intersection between the plane 3x-y+2z+1=0. and: a) the line x = s, y = -1 + 2s, z = -3…
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Q: Q2/ Let Li be the line through the points (1, 2, 6) and (2, 4, 8). Let L2 be the line of…
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Q: 52. The plane passing through the point P,(0, 2, -2) that is parallel to the plane 2x + y-z= 1
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Q: Find an equation of the plane. the plane through the point (8, −3, −4) and parallel to the plane…
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Q: cquation o Uie Ie V Are the plane 2x-y-4z = 10 and the line {x = 2+4t, y = 5- 2t,z =-8t} parallel or…
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Q: 4. Using two methods find the point point P = (5, 4, 4) on the plane x +y + z = 4 nearest the %3D
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Q: 1-y 2 Consider the plane π : x - 2y + 3z − 1 = 0 and the line 1: x= 1. Find the point of…
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Q: Find the plane determined by the intersecting lines. L1 x = - 1+t y = 2+ 4t z= 1-t L2 x = 1 - 4s y =…
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Q: 3. PQ lies in the standard (x, y) coordinate plane. What are the coordinates of the midpint of PQ if…
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Q: Find the point at which the line x = 2 – t, y = 1+ t, z = 4t intersects the plane x - y + 3z = 11.…
A: Given,
Q: trahedron enclosed by the coordinate planes and the plane x+2y+z= 8.
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Q: 17. projection of the line Find the equation of the 3x-y + 2z-1=0 = x +2y-z-2 on the plane 3x +2y +…
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Q: ) fnd the equ. f Plane that Contains the two line S: X-1=3+ 6=そ X-リ=Z-4 and Passes through origin?…
A: Given problem:- find the equation of Plane that contains the two lines x - 1 = y + 6 = z , x= y =…
Q: Tangent of x²2/3 + y2/3 + z²/3 = a²/3 surface at any point (Xo , Yo ,Zo ) Show that the sum of the…
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Q: Q.2C) In the xyz-plane determine the distance and angle from point (2,1,1) in the space and two…
A: We have to solve given problems:
Q: Find the intersection of the two planes with equations 3(x – 1) + 2y + (z + 1) = 0 and (x – 1) + 8y…
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Q: 9. The line through (0,-7, 0) perpendicular to the plane x + 2y + 2z = 13
A: Given point is (0,-7,0) and plane equation is x+2y+2z=13 here we have to find the parametric…
Q: Q1): Find the point (x, y, z) that lines on the plane x + y + 2z = 4 that is near origin.
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Q: 7. Find the point of intersection between the plane. I - y – z = 5 x +y + z = 1 5x – y + 2z = 17 (a)…
A: We have, the system of equations for plane as x-y-z=5 ⋯⋯1x+y+z=1…
Q: The plane perpendicular to the x-axis at (–2,0, 0) : The plane perpendicular to the y-axis at (0,…
A: the equation is (x1,y1,z1)=passing points a(x-x1)+b(y-y1)+c(z-z1)
Q: Solve the problem. Find the point on the plane x + 2y - z = 12 that is nearest the origin. Lütfen…
A: The given equation of plane is: x + 2y - z = 12
Q: 25. Find the intersection of the line [x, y, 2] = [1,4, – 2] + 1(1, – 1,3] and the plane 2r – 4y +…
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- Fast pls solve this question correctly in 5 min pls I will give u like for sure Anu Find a plane containing the LINE {x(t)=7-3t, y(t)=-8+3t and orthogonal to the plane 7x+7y+z=1, z(t)=-6+3tSteepest ascent on a plane Suppose a long sloping hillside is described by the plane z = ax + by + c, where a, b, and c are constants. Find the path in the xy-plane, beginning at (x0, y0), that corresponds to the path of steepest ascent on the hillside.Determine the location of a point (x, y, z) that satisfies the condition. x > 0 a) The point is behind the yz-plane. b) The point is behind the xz-plane. c) The point is in front of the yz-plane. d)The point above the xy-plane. e)The point below the xy-plane. f)The point is in front of the xz-plane.
- IV. Consider the plane : x + 3y - 2z = 6 and the line with parametric equations l: x=4-3t, y = 2+t, z = 2t. Find a general form of the equation of the plane perpendicular to and containing l. Point of intersection of plane and line : (1,3,2)Consider a plane P1 : 6 x− 3 y+ 6 z= 10. The plane P1 is perpendicular to a plane P2 . The points A:(3,2,0) and B:(2,−2,1) lie on plane P2. The scalar equation of plane P2 is:A family of orthogonal planes Find an equation for a family of planes that are orthogonal to the planes 2x + 3y = 4 and -x - y + 2z = 8.
- 22. a) Determine the equation of the line of intersection of planes 1 and 2. Express your answer in the form: [x,y,z] = [x0,y0, 0] + t[a, b, 1], b) Find the point where the line crosses the xz- plane. ?1: 2? + 2? − 3? + 7 = 0 ① ?2: 4? + 7? − 5? + 11 = 0 ②Find the coordinates of the point. The point is located in the yz-plane, seven units to the right of the xz-plane, and eight units above the xy-plane. (x, y, z) =Find an equation of the plane. The plane through the points (0, 9, 9), (9, 0, 9), and (9, 9, 0) Find an equation of the plane. The plane that passes through the point (2, 3, 4) and contains the line x = 4t, y = 2 + t, z = 3 − t
- 4. [V] Find a parametrization of the plane that contains both the point (2, 4, 6) and the line x = 7 − 3t, y = 3 + 4t, z = 5 + 2t.1) Let A = (0, 0, 0) and B = (2, 0, 0). a) Find a point C in the xy-plane that is a distance 2 from both A and B. b) Find a point D in 3-space that is a distance 2 from each of A, B, and C. c) Describe the figure obtained by joining A, B, C and D by straight lines.