9.) Let E be the tetrahedron with vertices: (0,0,0), E is bounded by four planes: z = 0, x=0, 2 3 (3,2,0) (a) V(E)= Y -2x + 3y = 0, 2x+6y +9z = 18.

Q: Q2 a) { ] Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = −20 represents a sphere, and find…

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Q: Consider the tetrahedron formed by the four points P(0, 0, 0), Q(8, 0, 0), R(0,6, 0), and S(0, 0,…

A: Given: A tetrahedron that passes through P(0,0,0), Q(8,0,0), R(0,6,0), and S(0,0,4). (a) To Find:…

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Q: 2) Calculate the distonce d of the pint ? (-l,(, -2) from the plane passing through the three A(…

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Q: a) [ ] Show that the equation 4x8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere, and find its…

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Q: 3. Determine the intersection (if any) of the following planes. Show your work clearly ₁: 2x + 3y z…

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Q: 19. Find the Cartesian equation of the plane a) passes through point A(6,- 7, 4) and parallel to the…

A: To find the Cartesian equation of the plane, a)Which passes through the point A6,-7,4 and parallel…

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: The point on the plane 2x+y+z=1 that is closest to the point (1, 2, 3) is (a, b, c). Then a+b-2c= O…

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Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

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Q: A: The plane Ax - By + Cz - 1 = 0 pass through non collinear points (1,1,0), (2,0,-1) and (2,9,2).…

A: Given that the plane  passes through non collinear points

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

Q: Among all the points on the graph of z= 12-x² - y² that lie above the plane x + 4y +62 = 0, find the…

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Q: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: 10) Use Green's Theorem to eualuate S+10ny +y?)dx + l6xy+ 5a²) dy Toxy+ sa?) dy where C is the…

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Q: (9) (a) Find the point P on the plane ry+2=-3 that is closest to the point Q(2, 3, 4). Is the point…

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Q: 2. Do the three planes X + 2y + z = 4, y - z = 1, x+ 3y = 0 have at least one commom point of…

A: The equation of the plane is given by the formula ax+by+cz+d=0. The system of planes can be solved…

Q: Suppose C is the triangle with vertices (3, 0, 0), (0, 4, 0), and (0, 0, 1) oriented…

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Q: Use Lagrange Multiplier to find the Point P (x,y,z) closest to the origin on the plane containing…

A: The equation of the plane passing through the three points can be obtained using the matrices. The…

Q: Compute ∮c (ydx+zdy+xdz) where C is the triangle with vertices (3,0,0), (0,0,2), and (0,6,0)…

A: The given points can be plotted as A(3,0,0) B(0,0,2) C(0,6,0)

Q: Calculate Sc (4(x²-y)i + 8(y² + x)}) · dr if: (a) C' is the circle (x − 8)² + (y – 5)² = 1 oriented…

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