43. Volume of a Parallelepiped Find the volume of the parallel- epiped determined by the vectors u = 2i - j, v = 2j + k, and w = 31 +j - k.

Q: Suppose that A, B, and C are the corner points of the thin triangular plate of constant density…

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Q: Find the work done in pumping gasoline that weighs 6600 newtons per cubic meter. A cylindrical…

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Q: Find the area of the surface. The part of the hyperbolic paraboloid  z = y2 − x2  that lies between…

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Q: 3) A vector is given as A = x(z+2)â,-()x+1)â, +(y+2)â. Prove the Stoke's theorem for the geometry…

A: From the below figure, ∮cA.dt=∫ABA.ds+∫BCA.ds+∫CDA.ds+∫DAA.ds Here ax=i, ay=j, ak=k Since…

Q: Hiw.2 Censider the PakullelePifed with šider: A=3i+2j+k Bziti+zkyczi+sj+3k;. thens t-Find the…

A: Given

Q: Find the coordinates of the centroid of the triangle enclosed by x = 1, y = 0, and y = 4x

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Q: 3. (.J 6) For two vectors u = [1,0,0]" and v = [1,1, 1]", find a third vector with unit length such…

A: Given: Lt us consider the given, u→=1,0,0v→=1,1,1

Q: A median of a triangle is a segment joining a vertex to the midpoint of the opposite side.…

A: The figure can be such that: Let the position vector of the vertices of triangle ABC be:…

Q: 3. Prove that a flat surface of revolution is part of a plane, cone, or cylinder.

A: prove that a flat surface of revolution is part of plane or cone or cylinder. solution a flat…

Q: Find the center of mass of a thin plate of constant density ô covering the given region. The region…

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Q: Volume of a Parallelepiped Refer to Problem 55. Findthe volume of a parallelepiped whose defining…

A: This formula for the volume can be understood from the above figure. The volume of the…

Q: lume of a tetrahedron with adjac 1 w is Ju· (v x w)| to determine 6. tices P(-3,2,0), Q(2, 1, –3), R…

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Q: plane π is said to be tangent to a spherical surface with center C and radius r if the distance from…

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Q: Q R U V

A: Centroid problem....

Q: Consider a unit disc of radius 1 centred at the origin. The straight lines y = x and y =-x break…

A: Plotting the y=x   ,   y=-x and  unit circle center at origin on the graph and dividing into TOP,…

Q: u=2i+4j+k   v=-i +3j+2k   w=i +5j-3k find u•v and v times w  also find the volume of the…

A: Given vectors are u=2i+4j+k,v=−i+3j+2k and w=i+5j−3k We have to find u⋅v,u×v and volume of the…

Q: usuƏp seu pin 100 kg/m and flowS With Ve Zk, whei y, and z are measurec in meters, and the…

A: Density of fluid=1100kg/m3 Flow with velocity v=xi^+yj^+kz^ To find the rate of flow outward through…

Q: Find the work done in pumping gasoline that weighs 6600 newtons per cubic meter. A cylindrical…

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Q: 1 Find equations in vector and rectangular form for the a) osculating plane, b) normal plane, and c)…

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Q: i. Find b × c in terms of λ . ii. Show that a · (b × c) is independent of λ .  iii. Find the…

A: i)

Q: Find the surface area of the portion of the sphere x2 + y2 + z2 = 25 inside the cylinder x2 + y2 =…

A: Recall:  The formula of surface area is S=∫∫S1+∂z∂x2+∂z∂y2 dA

Q: 6. In triangle FGH, F(6,-1), G(12,4), H(15,-2) with centroid M and midpoints L, K, J midpoints of…

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Q: A- Find the value of the constant (a) such that the volume of the paralleiepiped determined by a-…

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Q: Find the work done in pumping gasoline that weighs 6600 newtons per cubic meter. A cylindrical…

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Q: Find the sphere's center and radius. 9x2 + 9y? + 9z2 – 18x + 54y + 74 = 0 center (x, y, z) radius

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Q: Consider a unit disc of radius 1 centred at the origin. The straight lines y = x and y= -x break…

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Q: A sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes…

A: Given :-  A sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes…

Q: . The distance of a point in the 3-D system from the origin a. is defined by the absolute value of…

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: Find the surface area of helioid equation (spiral ramp vith vector r Cu,v) = LucosV, usinv, v). %3D

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Q: Volume of Cylindrical Coordinates

A: Query- Volume of cylinderical coordinates. Answer- The volume of the cylindrical coordinate is…

Q: a) If u and v are two orthogonal vectors with ||u|| = ||v|| and ro (x0, Y0, z0), show that r(t) : =…

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Q: Find the work done in pumping gasoline that weighs 6600 newtons per cubic meter. A cylindrical…

A: Given that a cylindrical gasoline tank 3 meters in diameter and 2 meters long is carried on the back…

Q: Find a non zero unit vecor ôv that is orthogonal to uz= (1,2,1) and Uz= (2,5,4) in R³.

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Q: Scoliosis is a lateral curvature of the spine that can be detected when a grid is superimposed over…

A: Given diagram on graph: Concept: Here to position a point, we shall determine the distance of point…

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: 14 Find the surfuce area the part of the parabolic cy linder 2=y? that the triangle with vertices…

A: According to the given information, it is required to find the surface area of the part of the…

Q: he volumes of the solids generated by revolving the regions bounded by the graphs of the equations…

A: We have to find the volume about the given lines.

Q: Replacement of the unit normal vector n by -n does not change the orientation of the surface. Select…

A: To check whether the given statement is true or false.

Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.

Q: a nonzero vector parallel to the line of intersection of the two planes x + 3y + 5z = -3 and x + 3y…

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Q: A sphere is inscribed in a straight circular cylinder. The sphere is cut by any two planes…

A: Now we will place the sphere at the origin and the cylinder  with the z-axis as it's central axis.…

Q: a. On a rectangular cartesian coordinate system, sketch the parallelepiped having the vertices (1,…

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Q: \lfu = i + j-k, v = 2i+j+ k, w = -i - 2j + 3k, find 1) The area of the parallelogram determined by…

A: Given u→=i+j-k,    v→=2i+j+k,   w→=-i-2j+3k   To Find: 1) The area of the parallelogram determined…

Q: Find an expression for a unit vector normal to the surface x = 8 cos (0) sin (4),y = 5 sin (0) sin…

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Q: The locus of points equidistant from two given parallel lines in space is

A: Given data:     The first parallel line is: l1. The second parallel line is: l2.   Parallel lines…

Q: n equation of the plane with normal vector n= (-3, –3, –9) passing through the point (-4, 7, –9) in…

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Q: 4. (8 points) Find a vector parametrization for the intersection of the plane x +y+z = 3 and the…

A: Use polar coordinates for Parameterization

Q: Find an expression for a unit vector normal to the surface x = 10 cos (0) sin ($), y = 5 sin (0) sin…

A: Given that x=10cosθsinϕ, y=5sinθsinϕ and z=cosϕ. We have to find a unit vector normal to the…

Q: A particle of mass m moves in a plane under the influence of a central force that depends only on…

A: Given that, A particle of mass m that is moving in central force,  Let the potential is Vr, Thus,…