1)calculate a*yz dædydz where D is the rectangular parallelepiped 1< « < 2,1 < y < 2,1 < z < 5

Q: Lo and Li are lines in 3-space whose parametric equations are Loix = x0 + aot, y = yo + bot, z = zo…

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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: Each point of the parallelogram is translated up 3 units and left 2 units and then connected to form…

A: After shifting parallelogram 3 units up and 2 units left the new parallelogram will be

Q: What is the distance between points (-6, -9) and (3, 3) on the coordinate plane? 8- 7- 6- 4- 3- 1…

A: Solve using co-ordinate geometry

Q: findthe parametríc equatlons for the line through the paint of in tersecti of the lines 4=X=2+ 36 14…

A: first we find intersection point of given line

Q: Q4\ Graph the curve r=1-cosx in Cartesion xy - plane

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Q: Describe the image of the line z = 1 + iy under the map flz) = sin z %3D

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Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-…

A: Solving two equations

Q: Find the length of the curve y? = r between the points (0, 0) and (4, 8)

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Q: Let S = R^2 - {(0, 0)} and let L be the set of all Cartesian lines lying in S. Show that {S,L} is…

A: We will use the definition of incidence geometry to solve the problem.By definition, a geometry…

Q: x-2 z+4 • Let L:*²=+3 = 2²+ and M: 2x - 3y +z = 6 are line and 3 2 5 plane and let P be the…

A: We have to find the equation of line

Q: Which three dimensional figures when sliced by a plane cannot have a cross section that is a square?

A: When a rectangular pyramid is sliced by a plane then the obtained section will not be square.

Q: .Calculate the dstance between tve point (3, -2) and the plane Z Xty-2+1=0.

A: The distance between the point (a, b, c) and the plane Ax+By+Cz+D=0 is given by,

Q: The plane ४/७ Incorrect y + + 6 4 SAPOR = 12 NIS = 1 intersects the x-, y-, and z-axes in points P,…

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Q: 8. Triangle BCD with verlices B(-2,3), C(8, 7), and D(-1,-5): y»x B' J C D'C

A: The given points are  B(-2, 3), C(8, 7) and D(-1, -5) And y=x We have to find B', C' and D' To find…

Q: b. Calculate its tangent line at (2,0) in the projective plane and verify the result by comparing it…

A: Please find the answer innext step

Q: Q4) Find the intersection of the line x = and the sphere x? + (y – 3)² + (z – 2)² = 4. A) (1,1,0) B)…

A: 1. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all…

Q: 2. Find the volume of the parallelepiped the following 3 vectors describe the edges: i.q=i-2j-3k, b=…

A: The given problem is to find the volume of the parallelepiped from the given following 3 vectors…

Q: 1. Find a parametrization of the line segment L from -2 to -2 + 2i. 2. Find the image of L under the…

A: We will find the equation for L and the image of L under w

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: 2. Find the area of a parallelogram defined by PQ and QR when P = (4, 0, 1), Q = (5, -3, 0), and R =…

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Q: Q1 find acubie palonemiat ofk given-points for27,3},(2,12)e

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Q: Find a vector function that represents the curve of intersection of the elliptic cylinder given by…

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Q: 10. The distance between the point (3,-2,5) and the plane 2x+2y+z=5 is NONE

A: Given: The distance between (3,-2,5) and the plane 2x+2y+z=5

Q: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

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Q: (10) Find the distance of (3,-1,2) from each of the following: a) line: x = 1+ 2t, y = -t, z = 1-t…

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Q: OShow that every point (b, c) in the plane lies on a tangent line to the graph of y = x³.

A: Consider the given information. y=x3 Find the derivative of the function. dydx=ddxx3y'=3x2

Q: Just like in a projective plane, two distinct lines always intersect on the spherical plane.

A: Straight lines in spherical plane are the great circles. So, any two different lines meets at two…