A- Find the value of the constant (a) such that the volume of the paralleiepiped determined by a- the vectors u=i+ak, y = 531 – 16i t ak. w = 20i+i-8k is 500. %3D

Q: 39. Find the surface area of the portion of the hyperbolic paraboloid r(u, v) = (u+ v) i + (u – v)…

A:

Q: (2.3) Prove that each of the following systems a) Parabolic cylindrical coordinates (u, v, z)…

A: The given question can be solved as shown in step2.

Q: A. If x and y are orthonormal vectors, then find the valne of x+ yl? - |x-yl

A:

Q: Evaluate ze*²+y²+z? dV, where E is the portion of the ball centered at the origin of radius 5, x2 +…

A:

Q: Consider the area bounded by the points P, (6,6), P2(8,4), and P3(12,4) Find the volume if it is…

A: Given area is a triangle with vertices 6,6, 8,4 and 12,4. And a line x=-3. The region with the line…

Q: Calculate the volume of solid S limited by the paraboloid z = 1 - (x² + y²) and the plane z = 0, as…

A: Volume of any solid is given by ∫∫∫dzdxdy=∫∫∫dzrdrdθ which is bounded by the region.  The the…

Q: a) Let i = xî + yj + zk, r = |7| and å is a constant vector. Find the value of %3D dxr div

A: We will find out the required value.

Q: Consider the parallelepiped with adjacent edges u = 5i + 9j + k v = i+j+3k w = i+ 5j + 7k Find the…

A: volume of the parallelepiped is given by  u→·v→×w→

Q: Q.14 The integral of the vector A(p, p, z) = "coso ô (standard notation for cylindrical coordinates…

A:

Q: Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and…

A: Given data: *The vertices of the triangle is (2,2), (2,7) and (4,7) From the coordinates of the…

Q: The masses m, are located at the points P;. Find the moments M and M, and center of mass of the…

A:

Q: Solve Sff, 3x² + 3y²dV by using cylindrical coordinates, where G is a solid in the first octant that…

A:

Q: What is equation of the plane passing through the point A(2, 1,3) and parallel to the vectors a = j-…

A: We have to find the equation of plane passing through point A(2,1,3) and parallel to vectors…

Q: How far is the centroid from point A? У-аxis - 25 cm - 30 cm 25 cm 30 cm 40 cm 25 cm - 30 cm 50 cm…

A:

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: 1. Find the area of the portion of the plane Зх — Зу + 2 — 12 that lies inside the cylinder y? + 22…

A:

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

A: Given, u=i+jv=j+kw=i+k

Q: What is the center of gravity of the solid formed when the plane region bounded by y^2 = 4x in the…

A:

Q: Let B be the ball with center at the origin and radius 1 SSS 4(z² + y² + z²)dV = B

A: Explanation of the answer is as follows

Q: Given point P(-2,6,3) and vector B= yax + (x+z)ay, Express P and B in cylindrical and spherical…

A:

Q: AP where R is the portion of the ball of radius 1 in 4-dimensions with all coordinates r, y, z, w 2…

A: I = ∫∫∫R∫ dvwhere R = portion of unit ball with x, y,z,w≥0I = ∫01∫01∫01∫01 dx dy dz dw= ∫01∫01yo1 dz…

Q: Find a unit vector normal to the plane containing v=i+3j-2k and w=-2i+j+3k.

A: There are two types of quantities that exist in nature, one is scalar quantity and the other one is…

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

A:

Q: implement Stokes ' Theorem by taking the vector function Å = (x² + z)i + (y² + x)j+ (z² + y)k on the…

A:

Q: Let B be the ball with center at the origin and radius 1 SS S2(z² + y² + z²)dV = %3D 8M 16x 5. 24x

A:

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

A:

Q: The equation of the plane that passes through the point P(1,0,0) and has the vector n = (0,0, 1) as…

A:

Q: SSx x dA; R is the portion of the disk x +y s 16 in the second quadrart

A: According to the given information, it is required to find the value of the given integral.

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

A: We have to find

Q: Consider the parallelepiped with adjacent edges Find the volume. V = i 102 u = 8i + 7j + k v = i + j…

A:

Q: 29. Using Pappus' theorem, the value of the y-coordinate of the centroid of a uniform semi-circular…

A: Pappus centroid theorem states that the volume V of a solid of revolution generated by revolving a…

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

A: Solution:-

Q: Determine the coordinates of the centroid of the shaded area. 25 y 70 I 50 25 60 60 50. 175…

A:

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

A:

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

A:

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

A:

Q: Which of the following is the volume of the parallelepiped determined by the vectors u=i+j-k,…

A:

Q: e of the solid by subtracting two volumes, the solid enclosed by the parabolic cylinders y = 1 − x2,…

A: Here we have to find the volume of the solid  by subtracting two volumes, the solid enclosed by the…

Q: Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and…

A: Using washer method

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

A:

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: Let B be the ball with center at the origin and radius 1 SIS 4(z² + y² + z*)dv = B

A:

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: 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: Vhich of the following is the volume of the parallelepiped determined by the vectors u=i+j-k,…

A: volume of parallelepiped V =( u * v ).w

Q: A. Find the volume of the region bounded above by paraboloid z = 5-x² - y and below by the…

A: Paraboloid is a three dimensional figure which is obtained when a parabola is rotated about its axis…

Q: Use cylindrical coordinates to find the vol- ume of the solid that lies within both the 2 cylinder…

A:

Q: On: A IS tor while A is a scalar. |A|. If A B < 0, then the (smaller) angle between the vectors A…

A:

Q: Let B be the ball with center at the origin and radius 1 SS $3(x² +y? + z²)dV = 16 12m 24m :5

A: