Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1 in the affine space and then in the projective space by using homogeneous coordinates. Complex solutions are valid.

Q: Graph the quadric surfaces given by the equations in Exer- cises 41–48. y2 41. x² = y? x2 42. z2 9.…

A: As per guidelines incase of multiple questions (or) multiple sub-parts asked we are supposed to…

Q: Find a parametrization for the line segment beginning at P,(4, - 7,- 7) and ending at P2(0, - 7,2).

A: The line segment beginning at P1<4, -7, -7> and ending at P2<0, -7, 2>

Q: 4. Prove that the midpoint of the line segment connect- ing the points (x 1, X 2, - . . , Xp) and…

A: The midpoint of a segment can be considered to be the average…

Q: Find a parametrization for the line segment beginning at P1 and ending at P2. 25) P1(-4, –5, 4) and…

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Q: Sketch the Surface z./4-x* and verify that fay -lyx.

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Q: Find the distance (in appropriate units) between the points P(2,−1)P(2,−1)and Q(3,4)Q(3,4)in the…

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Q: Prove that the line x +1 = 글(-6) - lies in the plane 3x + y – 2 = 3.

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Q: What kind of conic section is given by the quadratic form ? -11x,2 + 84x,x2 + 24x,2 = 156 Transform…

A: Given Quadratic Equation is, -11x12+84x1x2+24x22=156 Matrix Representation form is, A=-11424224 Find…

Q: 4. Find a plane through Po(2, 1, –1) and perpendicular to the line of in- tersection of the planes…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10.

A: Given,           The distance between the point 2,-4,3 and the plane 5x-2y+z=10.We know that,…

Q: Find the shortest distance from the point (1, 5, -5) to the plane 2x + 9y - 3z = 6, using two…

A: Given point is 1,5,-5 and plane is 2x+9y-3z=6

Q: 4) Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0,…

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Q: Find the orthogonal trajectories of the family of circles with center at the point (0, 1) and radius…

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Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

Q: 14) Determine the distance between the parallel planes: 6z = 4y – 2x; and 9z = 1 – 3x + 6y.

A: Given:-planesP1: 6z=4y-2x2x-4y+6z=0x-2y+3z=0P2: 9z=1-3x+6y3x-6y+9z=1x-2y+3z=13To find : distance…

Q: Determine whether the planes 3x−4y + 5z = 0. and −6x + 8y−10z−4 = 0 are parallel.

A: The given planes are, 3x-4y+5z=0 and -6x+8y-10z-4=0

Q: Verify Green's theorem in the plane for M = -2y and N = x , where C is the semi circle x2 + y? = 9,…

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Q: A. Show that the planes (x+y- z = 1) and ( 2x - 3y + 4z = 5 ) are neither parallel nor…

A: Let's find.

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: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: Prove that the circles x² + y2 + z2 - 2x + 3y + 4z - 5 = 0, 5y + 6z +1 = 0 x² + y2 + z2 - 3x - 4y +…

A: We will use equation of sphere passing through sphere S  and plane P  S+λP =0

Q: 2 b) Prove that Imz=0, larg z - 41= 4, 2-ž =0, 1Z-il=1Ztil are different equations all describing…

A: If we let z=x+iy then We will show that y=0 which is the equation of real axis.

Q: 2. Find the plane that is orthogonal to the line : +1 = 431 = z and contains the point where l…

A: line parallel to the vector  V=⟨a,b,c⟩ passing through the point (x1,y1,z1) is given by the…

Q: 7. Find the distance between the point (3, 1, –2) and the plane x + 2y – 2z = 4.

A: Given that plane x+2y-2z=4 and point 3,1,-2To find :Distance between point and plane Solution if…

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: Find the distance between the planes. 5x-2y+z-4 0, 5x-2y+z+6= 0

A: Given,  Equation of Plane 1: 5x - 2y + z - 4 = 0 Equation of Plane 2: 5x - 2y +z + 6 = 0 From the…

Q: Sketch the surface 2./4- and verify that fry - lyx

A: Given surface is  z=4-x2-y2 we have to sketch this and verify that fxy=fyx

Q: Use Green's theorem to calculate where C is the rectangle with vertices (0, 0), (2, 0), (2, 3), (0,…

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Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

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Q: Sketch the surfaces PARABOLOIDS AND CONES x = 4 - 4y2 - z2

A: The given equation is x = 4 - 4y2 - z2

Q: 2. Use analytic geometry to verify that quadrilateral JKLM is a parallelogran 1C). YA K(-1,1) 2 -2 0…

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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: Reduce the equation    4x^2 + y^2 + 4z^2 - 4y − 24z + 36 = 0    to one of the canonical forms of…

A: Reduce the equation    4x^2 + y^2 + 4z^2 - 4y − 24z + 36 = 0    to one of the canonical forms of the…

Q: Find 3 non-collinear points in the plane ax+by+cz+d=0. (Hint: Set two variables to zero for each…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Hiwed Find equations for_thefallawing lines - The line through (3, Sz=2) Perfendiculor toX-z plane

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Q: find the pole and resuidue of 3z + 1 (z + 1)(2z – 1)

A: Poles and residue of the given function are given below ;

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: Determine the distance from point Q = (2, 6, 9) to the plane x + 2y + 2z = 8

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Q: Find the distance between the planes 4x + 6y – 2z = 4 and –2x – 3y + z = -3.

A: We have to find out the distance between two planes

Q: Find the shortest distance between (3,4,1 ) and the plane X+y +Z = -2

A: Using distance between plane and point formula we can calculate.

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: Discuss the hyperbolic geometry of spacetime in comparison to circular geometry of 3- vector space.

A: Query- Discuss the hyperbolic geometry of spacetime in comparison to circular geometry of 3- D…

Q: Determine the set of points satisfying the condition described by |z – 3| + |z + 3| = 10 Then…

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Q: Pind all point on 2=8-3x°- 243 where ohe bonyent plane is orehogonal :2-36,リ=タ +&e, 2-5-ビ to the…

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Q: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…

Q: Find the point at which the line 7(t) = +t intersects the xy plane. %3D

A:

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.…

Q: The distance between the centers of the following two spheres: x2+56x+y2−54y+z2=−1512,…

A: A detailed solution is given below

Q: Show that the two planer diagram represent the homeomorphic surfaces

A: Given:-                 Show that the two planer diagram represent the homeomorphic surfaces