Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2,1,0) Q(2, 3, 2)…
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Q: Show that the volume V of a parallelepiped having u, v, and w as adjacent edges is V = ∣u ∙ (v ×…
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Q: Consider the right triangle withvertices (0, 0), (0, b), and (a, 0), where a > 0 and b > 0.…
A: Given right angle triangle has vertices (0, 0), (0, b), and (a, 0), where a > 0 and b > 0.…
Q: Find the volume of the parallelepiped whose adjacent axes PQ, PR and PS where P (1,-2, 2), Q (1, -1,…
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Q: Consider the parallelepiped with adjacent edges u = 6i + 4j + 2k; v= 2i + 2j + 4k; w = 2i + 6k + 6k…
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Q: Find the volume of the parallelepiped having adjacent edges u, v, and w; for u = (1,-1,0), v =…
A: Given u=1,-1,0, v=0,2,2 and w=1,3,1
Q: Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k, v…
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Q: The volume of the pyramid formed in the first octant by the plane 6x + 10y + 5z-30 = 0 is: О 45 О зо…
A: We can solve as follows
Q: Calculate the volume of the parallelepiped spanned by u = (2, 2, 1), v = (1,0, 3), w = (0, -4, 0)
A: u→=<2,2,1>v→=<1,0,3>w→=<0,-4,0>Volume of…
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: Find the volumes of the regions. The wedge cut from the cylinder x2 + y2 = 1 by the planes z = -y…
A: Given Data The equation of a cylinder is x2+y2=1. z=-yz=0 Determine the interval of x and y,…
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 u, v, and w in the Figure below.
A: u=(1,0,4) v=(1,3,1) w=(-4,2,6)
Q: Find the volume of a parallelepiped whose edges are ä = 7i+5j-k, 6-j+4k and e= 4i-3j+6k %3D
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Q: Consider the parullelepiped with Sider. t-Findthe Volume of the Paralletefiped 2 Findthe…
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Q: Find the area of the portion of the surface z = 8x+4y that lies above the triangular region with…
A: Thanks for the question :)And your upvote will be really appreciable ;)
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 area of the part of the surface z = x² + 2y that lies above the triangle with vertices…
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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: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2,1,0) Q(2,3, 2)…
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Q: Find the distance between the parallel planes 4x – 3y + 12z = 12 and 4x — Зу + 12z 36.
A: In this problem we have to find distance between two parallel planes.
Q: Consider the parallelepiped with adjacent edges Find the volume. u = 2i + 7j + k v=i+j+7k w = i +4j…
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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1, 0) Q(2, 3,…
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Q: Use cross products to find the area of the quadrilateral in the xy-plane defined by (0, 0), (1, −1),…
A: Let vertex of Quadrilateral are O(0,0), P(1,-1), Q(3,1) and R(2,4) Area of the…
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: Use cross products to find the area of the triangle in the xy-plane defined by (1,2), (3,4), and…
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Q: Find the area of the cap cut from the sphere x2 + y2 + z2 = 2 by the cone z = √(x2 + y2).
A: to find the area
Q: Find the volume of the parallelepiped with adjecent edges PQ, PR and PS; P(-2,1,0), Q(2, 3, 2), R(1,…
A: Volume of the parallelepiped: The volume of the parallelepiped is equal to the…
Q: Show that the area of the plane region bounded by the curves, x - y =7 and x= 2y² - y + 3…
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Q: Find the surface area of the part of the plane 7+ 2x + 5y that lies above the rectangle [1, 4] x [0,…
A: Given that Z=7+2x+5y To find the area of the surface of the plane that lies above the rectangle
Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…
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Q: Find the area of the region formed by the lines: * - y, x = Jy, y = 0, y = 2 %3D O1.562 square units…
A: Explained below
Q: Find the volume of the parallelepiped spanned by u = (1, 0, 4), v = (1, 2, 1) and w = (-4, 2, 9) in…
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Q: Find the distance between the planes 4x + 5y + z = 25 and 4x + 5Y + z = 53. %3D
A: Explanation of the solution is given below....
Q: Find the surface area of the portion of the cone x² + y² = z² above the region inside 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=<1,3,1> v=<0,6,6> w=<-4,0,-4>
Q: Find the volume of the box (parallelepiped) that is determined by u = i + 2j - k, v = -2i + 3k, and…
A: Solution:- The given vector is u→=i+2j-kv→=-2i+0j+3kw→=0i+7j-4k
Q: Find the volume of the parallelepiped with adjacent edges t = 3j – 4j – 6k, u = 3i – 7j – 7k and v =…
A: t =3j–4j–6k, u=3i–7j–7k and v=5i+ j+3kTo find the volume of the parallelepiped
Q: Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and…
A: Using washer method
Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2,1,0) Q(2,3, 2)…
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Q: Find the absolute maximum and minimum values of f(r, y) = r-3r-y+12y, closed region D, where D is…
A: Given problem:- Find the absolute maximum and minimum values of f(x, y) = x²-3x-y³+12y, on the…
Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1, 0) 2(2, 3,…
A: Follow next step
Q: Find the surface area of the part of the plane 3x + 3y+ z = 9 that lies above the triangle formed by…
A: In the question we have to find the surface area of the plane.
Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1,0) Q(2, 3, 2)…
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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: Calculate (x+ y)dA, where Ris a triangular region with vertices (0,0), (3,0) and (3,3).
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Q: 2) Find the area of the part of the surface z = x2 + 2y that lies above the triangle with vertices…
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- Calculate ∫C y2 dx -yz2 dy - sen(z)dz, where C is the path connecting the point A(−2,2,4) to the point B(1,2,2) by the parable z=x2 on the plan y=21) Draw a picture of two spheres of different sizes being tangent to each other at exactly one point P in R 3 . Do NOT put one sphere inside the other one. 2) Suppose we have two surfaces S1 and S2 which intersect at some point P = (x0, y0, z0), and further suppose that the normal vectors n1 =‹a1, b1, c1› (for S1) and n2 = ‹a2, b2, c2›(for S2) at P are parallel (and non-zero). Prove that the tangent planes TPS1 and TPS2 are the same by transforming the scalar equation for TPS1 into the scalar equation for TPS2. Hint: This should be a one-step algebraic transformation based upon using the algebraic definition of parallel vectors.In Problem ,use the vectors in the figure at the right to graph each of the following vectors. 3v + u - 2w
- Consider the following geometry problems in 3-spaceEnter T or F depending on whether the statement is true or false. 1. Two lines either intersect or are parallel 2. A plane and a line either intersect or are parallel 3. Two planes orthogonal to a third plane are parallel 4. Two lines orthogonal to a third line are parallel 5. Two planes parallel to a line are parallel 6. Two lines parallel to a third line are parallel 7. Two lines parallel to a plane are parallel 8. Two lines orthogonal to a plane are parallel 9. Two planes orthogonal to a line are parallel 10. Two planes either intersect or are parallel 11. Two planes parallel to a third plane are parallelFind the point on the graph of z = 2x^2 − 3y^2 at which vector n=⟨8,−12,1⟩ is normal to the tangent plane.If v = (1,2 ) draw all vectors w = (x, y) in the xy plane with v · w = x+ 2 y = 5. Why do those w's lie along a line? Which is the shortest w?
- 4. Draw a set of orthogonal 2d axes and illustrate the play that intersects at X=1/4, Y= 1 and Z=1/2 Calculate the Miller indicesSuppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find an equation of the plane tangent to the surface z = ƒ(x, y) at the point P0(1, 2, 4).5. Find the volume of the parallelepiped determined by the vectors a = i + j, b = j + k, and c=i+j+k 6. Given that P(3,0,1),Q(−1,2,5),R(5,1,−1), and S(0,4,2). Find the volume of the paral- lelepiped with adjacent edges PQ,PR, and PS. 7. Given that P (1, 1, 1), Q(2, 1, 3), and R(3, −1, 1) are vertices of a triangle. (a) Find the area of the triangle determined by the points P, Q, and R. (b) Find a unit vector perpendicular to plane PQR. 8. Leta=i+2j−k,b=−i+j+k,andc=i+k.Whichvectors,ifany,are (a) perpendicular? (b) Parallel? Give reasons for your answers.
- For vectors in the unit circle 11 x 11 = 1, the vectors y = Ax in the ellipse will have 11 A -l y 11 = 1. This ellipse has axes along the singular vectors with lengths = 0"1, ... , O"r (as in Figure 7.5). Expand IIA-1 Yll2 = 1 for A= [2 1; 1 2].Suppose that z is an implicit function of x and y in a neighborhood of the point P = (1, 1, 0) of the surface S of the equation: xy + yz + zx = 1 An equation for the line tangent to the surface S at the point P, in the direction of the vector w = (1, −2), corresponds to: The answers are in the attached image.10.Suppose that each of the vectors x(1), …, x(m) has n components, where n < m. Show that x(1), …, x(m) are linearly dependent. In each of Problems 11 and 12, determine whether the members of the given set of vectors are linearly independent for −∞ < t < ∞ . If they are linearly dependent, find the linear relation among them.
