Let W1, W2 be planes in 3-space defined by equations W1 : 21 – 2x2+ 3x3 = 2, W2 : x1 – x2+ 4x3 = 3. Find the parametric form of the line of intersection of these planes: + t

Q: Choose a set S of three points such that aff S is the plane in R3 whose equation is x3 = 5. Justify…

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Q: Find parametrizations for the lines in which the planes 5x - 2y = 11, 4y - 5z = -17

A: Given: The given two planes  5x-2y=11 and 4y-5z = -17 are intersects.

Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis…

A: Here given figure is Since prism has 5 surfaces (1)-OAB (2) OADE (3) CDE (4) OBCD (5) ABCE

Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-plane.

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Q: O Find the distonce from the point pC1,\, 1) to the plane 2K-3y+72=1

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Q: Let T be the plane x – y – z = 7. Which of the following planes are orthogonal to T and pass through…

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Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: Find the distance between the planes 5x - 3y + z = 9 and 5x 3y + z = -2.

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Q: Let W1, W2 be planes in 3-space defined by equations W1 :¤1 – 2x2 + 3x3 = 2, W2 : x1 – x2 + 4x3 = 3.…

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Q: Prove that the planes determined by the equations ax + by + c z = d and αx + β y + γ z = δ are…

A: Given planes, ax + by + c z = d αx + β y + γ z = δ

Q: Find a parametrization of the line in which the planes x+y +z= -2 and y +z= 6 intersect.

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Q: Which of the following points is on the xy and yz planes, but is not on the xz plane? a) (2, 0, 0)…

A: We can represent 3D coordinate system.

Q: If 1x, y2 are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

A: If (x,y) are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

Q: A sphere of constant radius r passes through the origin O, and cuts the axes in A, B, C. Prove that…

A: Given: Equation of the sphere with origin at O x2+y2+z2-ax-by-cz=0→1The radius of the sphere is…

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane z + 2y +…

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

A: Solution

Q: Find all planes in R3 whose intersection with the xz-plane is theline with equation 3x + 2z = 5.

A: Find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

Q: Find the symmetrical point of point P(1, 3, 4) with respect to the plane D:3x-2y+z+6=0.

A: Symmetrical point at plane problem....

Q: Let L be a line which passes through the point (-6,0, 1) and is perpendicular to the plane r + 2y +…

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Q: Find the point Q symmetric to the point P (1; 3; —4) with respect to the plane 3x+y-2z=0

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Q: Find the point p(x, y, z) on the plane 2x + y - z - 5 = 0 that is closest to the origin.

A: Given:The given plane is 2x+y-z-5=0 that is closest to the origin.To find:we have to find…

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: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Find a parametric representation of the line through the point P(3,1,-4) and perpendicular to the…

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Q: Find the trace of the plane in the given coordinate plane. Зх — 9у + 82 %3D7, yz

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Q: Зх + 2у + 3z %3D 6

A: Use a graphing utility to plot the graph of 3x+2y+3z=6 .

Q: Find the distance from the point B = (1, 0, 2) to the plane P whose general equation is x + y -z =…

A: Equation of the plane is Given point is

Q: Find an equation of the plane in standard form (ax + by + cz = d) that passes through the point (4,…

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Q: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane r+ 2y +…

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Q: Let L be a line which passes through the point (-6,0, 1) and is perpendicular to the plane x + 2y…

A: Direction ratio of Line is < 1,2,6> Write equation of straight line and solve it with plane to…

Q: 9. Suppose that a : R³ → R³ by perpendicular projection onto the plane 3x – 2y + z = 0. Find ↑

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Q: The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. Show that the planes are orthogonal.

A: Given: 3x+6z=12x+2y−z=3

Q: Find the projection of a on the plane P if a 4 and P has the equation x + y + z = 1.

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Q: Find parametrizations for the line in which the planes 3r- 6y – 2z = 3, and 2x+y-2z = 2 intersect.

A: Given Equation of planes 3x-6y-2z=3 and 2x+y-2z=2

Q: Verify that the line r(t) = [1 + t, 1 - t, t] is part of the one sheeted hyperboloid x^2 + y^2 -…

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Q: Which of the following represents a plane surfac whose x-, y-, and z-intercepts are a, b, and c…

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Q: Find the distance from the point of intersection of liies ( X=t, y=3-3t, =-224) and (x=1+t y=4rt,…

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Q: Let L be a line which passes through the point (-3, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: 3. Show that every sphere through the circle x2 +y-2ax+r²=0, z=0 cuts orthogonally every sphere…

A: This is a co-ordinate geometry problem

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1:  x=1+t, y=1+6t, z=2tLine L2:  x=1+2s, y=5+15s, z=-2+6s

Q: Find parametrizations for the lines in which the planes x - 2y + 4z = 2, x + y - 2z = 5

A: Given the planes :- x - 2y + 4z = 2,  x + y - 2z = 5   The Arbitrarily set z =1 and solve the…

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let P be the plane with equation −x+2y−2z = 3. Find four distinct points on P at distance 3√10 to…

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Q: Find the point on the plane 2x + 5y + z =9 that is nearest to (2,0,1). Vhat are the values of x, y,…

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Q: Suppose that II1 and II2 are parallel planes in R³, given by: II : ajx + biy +cjz = d1, and II2 :…

A: If ∏1: a1x+b1y+c1z=d1 and ∏2: a2x+b2y+c2z=d2 are parallel planes, then, the cross product ∏1×∏2=0.…