Q:- find the line of interseetion o f the given by 3X +6y -SZ=-3 S the plane plane -2x + 7y -Z=24 1) %3D

Q: Q5/ find the equalion of bhe plane that Condains the Line: x-!= +!2= and the Point A(5,1,) %3D 2.

A: See the attachment

Q: The two planes r+y +z= 1 and r – 2y + 3z = 1 intersect in a line l.

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Q: Q4. Find an equation of a plane that contains the line x=t, y=1+2t, z=2-t.

A: We have to find the equation of plane .       According to our guidelines ,we cannot solve all…

Q: Evaluate x² zdS, where S is the part of the plane z = 3 + 4x + y above the rectangle [0, 4] × [0,…

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Q: Q4/ A) Given the two planes 2x-3y+z-7 and 2x-3y+z=11. Find the following: 1- Approve that these…

A: Two planes are given and we need to solve the given questions for the planes.

Q: Find the point at which the line x(t) y(t) z(t) - 5+ 5t -6-8t intersects the z plane. - 7+8t

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Q: Above the paraboloid z= 6-x-y² and under the plane z= 9 for x? +y? < 4 .

A: volume by double integral using  polar coordinate

Q: Q2/ Find the equation of the plane through the point (2, 4, 5) perpendicular to the line: X=5+t,…

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Q: Evaluate / x2 zdS, where S is the part of the plane z = 4+ 3x + y above the rectangle [0, 4] x [0,…

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Q: (a) Find an equation for the line of intersection between the planes x+3y–z= 2 and 2x –y+2z = 5. (b)…

A: Given: Two planes  x+3y-z=2vector a = &lt;1 , 3 , -1 &gt;2x-y+2z=5vector b = &lt;2 , -1 , 2 &gt;

Q: Q8) The distance between the line x=-1+t, y=3+2t, z=-t and the plane 2x- 2y-2z=3 is: * 5 -units V12…

A: In a three dimensional picture, the line and plane are drawn as per their equations. It is desired…

Q: Q8) The distance between the line x=-1+t, y=3+2t, z=-t and the plane :2x-2y-2z=3 is

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Q: Determine the equation of the perpendicular bisector of KL if it's endpoints are at K O-7,5) and…

A: Given:    Points : K ( 7 , 5 )    ,   L ( 9 , 1 )

Q: Evaluate ffz + 3y - x^2 ds where S is the portion of z=2-3y+x^2 that lies over the triangle in the…

A: To find the value of given fds over given region.

Q: Q8) The distance between the line x=-1+t, y3D3+2t, z=-t and the plane 2x-2y-2z=3 is: *

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Q: FInd the x-intercept of the plane 2x+5y+z=10

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Q: Explain.

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Q: Q4:Show if the line (x = 5y +17, y+z-2= 0) lies in the plane 3x-41y-26z +1 = 0 or no ? Where does…

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Q: 3. Explain what is wrong with the following statement: If R,T are corresponding regions in the xy…

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Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0.

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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: Find the coordinates of the point where the line F = (1+21)î + tĵ – 2tk intersects the plane 2x – y…

A: Let's find.

Q: The line L(t) = (4 – 3t, 3, 1 +t) intersects the plane 3x – 3y + 2z = -16 at the point when t =

A: To find the point of intersection of the line and the plane, substitute the values of x,y, z from…

Q: 9-The distance d between the parallel planes -2x+y+z 0, 6x-3y-3z-5-0 is: a) V54 b) 54 V5 d) 3 c) e).…

A: Distance between two parallel lines

Q: 2. Assume that the plane P3 is perpendicular to the yz-plane, and the line l2 : x = 2t, y = t, z =…

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Q: H.W: Find the point where the line y=-2t, 1+t intersects the plane 3x+2y +6z 6

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Q: Show that D = |d1-d2l Vaz+b2+c2 P+1 represnts the distance between the parallel planes ax + by + cz…

A: Please refer the attached image for complete solution.THANK YOU.

Q: Find the point at which the line r(t) y(t) z(t) = -6-7t 7+t - 54t intersects the z plane.

A: Let's find intersect points.

Q: Fud the Line pussing through the posnt (!,-l,o) and purrllel to the Eme of intersection of planes (X…

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Q: 2. Trapezoid QRST with vertices Q(3. 1). R(5. 2), S(10, 0), and T(4,-3); 270° counterclockwise about…

A: GIVEN Trapezoid QRST with vertices Q(3,1),R(5,2). S(10,0) and T(4,-3); 270 counterclockwise about…

Q: ind an equation of the line of intersection of the following two plane x + y + z = 0 nd 2я — у + 32…

A: We have to find out

Q: Which point(s) lie in the plane 2x + 3y + 4z = 24? a) (0, 0, 6) c) (4, 4, 1) b) (0, 3, 4) d) (-2, 6,…

A: Given: 2x+3y+4z=24 For finding which point lie on given equation of plane, we put each point on…

Q: c. Find the distance from Po = (3,9, 6) to the plane 3.x + 4y – 5 = 0.

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Q: The wedge cut from the cylinder, x2 + y? =1 by the planes, z = -y and z = 0. Set up only

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Q: Q/ Find the angle between the planes (x+y+Z=1)and (x-2y+32=1). And find the Symmetric equations for…

A: We have to find angle between two planes

Q: The line L(t) = (2+1,8-31, 2t-6) intersects the plane 2y - 3x + 3z = -11 at the point

A: Given, the line             Lt=2+t, 8-3t, 2t-6                                   ...(1) Intersects…

Q: lo. find a point in the plane x+2y+3z=13 nearest to the point (1,1) usung the methed of Lagrange's…

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Q: Q:- find of the the line of interscetion plane given by 3X +6y -S2=-3 f the plane -2x + 79 -2=24

A: 3x+6y-5z+3=0 -2x+7y-z-24=0 Let z=t 3x +6y = 5t-3 -2x+7y = t+24

Q: Q2) L, - X+2 +2 ー1 - 2 Frand equaton of plane Coudentg

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Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

A: The line x(t)=2+4t, y(t)=-6-8t, z(t)=6-7t intersect yz plane Note:    Multiple questions are given,…

Q: Q2:Prove that the line (x-1)/2=(y+1)/3=(z-2)/(4 ) is parallel to the plane x-2y+z=6 ?

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Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0. %3D

A: Distance between parallel planes d=(d2-d1) /(sqrt(a2+b2+c2)

Q: Find the line of intersection of the planes x + 7y + z = 9 and x − 5y + 4z = 15

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Q: B. If the two planes ax-4y - 9z = 4 and perpendicular. Find the value of a. x-2xy + 3z = 1 are

A: Topic = Geometry

Q: WZ is the midsegment of the trapezoid UVXY. If XY = 6t, WZ = 10t – 2, and UV = 6t + 4, what is the…

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