Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v, and w. U =i+j V =j+k w = i+k

Q: Use the new command from Example 3 above to find the volume of the parallelepiped formed by vectors…

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Q: Consider the parallelepiped with adjacent edges u = 4i + 3j + k v = i+j+ 4k w = i+ 9j+ 2k Find the…

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Q: Let u = i−5k, v = 2i−4j + k,and w = 3i−2j + 5k. (a) u · (v × w) = ______. (b) The volume of the…

A: Given :           u = i - 5k , v = 2i - 4j + k, w = 3i - 2j + 5k

Q: Consider the parallelepiped with adjacent edges u = 7i + 7j + k v = i+j+ 3k w = i+ 7j + 5k Find the…

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Q: Consider the parallelepiped with adjacent edges u = 8i + 6j + k v = i+j+ 2k w = i+ 6j + 3k Find the…

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Q: Prove that the volume of the sphere x² + y² + z² = a² is V =÷na³

A: In this question, we find the volume of sphere by using triple integral

Q: Use the disk method to verify that the volume of a sphere is 4/3 πr3 , where r is the radius ?

A: So sphere is basically a circle that is rotated through the x-axis. We will suppose to cut a disk…

Q: Find the surface area of the tetrahedron bounded by the coordinate planes and the plane 8x + 12y +…

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Q: Evaluate the volume between the surfac x²y, and the rectangle in the xy 2 = plane given by 2 < x <…

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Q: Find the volume of the solid enclosed by the paraboloid z = 4 + x2 + (y – 2)2 and the planes z = 1,…

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Q: Consider the parallelepiped with adjacent edges u = 4i + 6j + k v = i+j+ 9k w = i+ 3j + 7k Find the…

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Q: Consider the parallelepiped with adjacent edges u = 5i + 7j + k v = i+j+7k w = i+ 8j + 7k Find the…

A: Volume of the parallelepiped is 238 cubic units.

Q: Use a scalar triple product to find the volume of the parallelepiped that has u, v, and w as…

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Q: Find the volume of the solid that is enclosed by the cone  z = sqrt(x2 + y2) and the sphere  x2 +…

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Q: Use triple scalar product of (u*v)*w to find the volume of the parallelepiped having edges…

A: The given vectors are u = i + j + k v = 9i + 3j +2k w = 8i + 10j + 5k

Q: Use polar co ordinates to find the volume of the given solid  above the cone z=sqrt{x^2+y^2} and…

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Q: Consider the parallelepiped with adjacent edges u = 7i + 3j + k v = i+j+3k w = i+ 8j + 6k Find the…

A: As per given question  We are going determine the volume

Q: Consider the parallelepiped with adjacent edges u = 9i + 6j + k v = i+j+7k w = i+ 6j + 6k Find the…

A: The given equations are,  u=9i+6j+k v=i+j+7k w=i+6j+6k.

Q: Find the volume V inside both the sphere x² + y² +z² = 1 and the cone z = V/x² + y².

A: Use the conversion formulas to write the equations of the sphere and cone in spherical coordinates.…

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges: u = i…

A: We have to find the volume of parallelepiped used the scalar triple product.…

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A: Find the volume of parallelepiped

Q: Find the volume of the parallelepiped (box) determined by u, v, and w. u V i+ 3j 4i - j+4k 2i + 4k

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the volume of the parallelepiped with adjacent edges t = 3j – 4j – 6k, u = 3i – 7j – 7k and v =…

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Q: Consider the paraboloid z = 1- ² – y?. Find the volume of the region between this surface and the ry…

A: According to the problem,. we have

Q: Use a scalar triple product to find the volume of the parallelepiped that has u, v, and w as…

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Q: Find the volume of the parallelepiped spanned by the vectors i +j+ k, i –j+k and 3k.

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Q: verify that (u * v) . w = (v * w) . u =(w * u) . v and find the volume of the parallelepiped (box)…

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

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Q: The volume of the parallelepiped is Volume = |a x b||c|| sin | = |(a × %3D b). c| True False

A: Using direct formula

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A: We have to find

Q: Find the volume of the sphere x? + y² + z² = a² (In Cartesian coordinate system).

A: To calculate the volume of the sphere, use the following formulae.…

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u = 2i…

A: We have to find the volume of parallelepiped using scalar triple product for the given adjacent…

Q: Find the area of the surface given by r(u, v)=9ui-vj+vk, where 0≤u ≤2 and 0 ≤ y ≤4. O 45√2 O 38/2 O…

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Q: Find the volume of the solid enclosed by the paraboloid z = 3 + x² + (y – 2)2 and the planes z = 1,…

A: Given z=3+x2+(y-2)2 and the planes z=1, x=-2,x=2,y=0 and y=2.

Q: Find the volume of the largest closed rectangular box in the first octant having three faces in the…

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A: Given, u=&lt;1,3,1&gt; v=&lt;0,6,6&gt; w=&lt;-4,0,-4&gt;

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

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Q: The volume of the parallelepiped is Volume = |a x b||c|| sin o| = |(a x b)- c| %3D %3D True False

A: We have to check either the volume of parallelepiped is volume=a×bcsinϕ=a×b·c or not.

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u = 3i…

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Q: Show that the volume of the segment cut from the paraboloid x2 /a2 + y2/ b2 = z/ c by the plane z =…

A: Show that the volume of the segment cut from the paraboloidX^2 /a^2 + y^2/ b^2 = z/ cby the plane z…

Q: Find the volume of the solid enclosed by the paraboloid z = 5 + x + (y - 2)2 and the planes z = 1, x…

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Q: verify that (u * v) . w = (v * w) . u =(w * u) . v and find the volume of the parallelepiped (box)…

A: Given that, u = i + j - 2k v = - i - k w = 2i = 4j - 2k Then we get the volume of the parallelepiped…

Q: (b) Prove the volume of a parallelepiped with a vertex at the origin and edges ü,v, and w is given…

A: In the question we have to prove the formula.

Q: Find the volume of the solid that is enclosed by the cone z = and the sphere x² + y2 + z2 = 72.

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