Consider the points A(1, –1, 2), B(2, –3,0), C(-1, –2,0), and D(2, 1, –1). | (a) Find the volume of the parallelepiped that has the vectors AB, AC, and AD as adjacent edges. NOTE: Enter the exact answer. Volume = 13 (b) Find the distance from D to the plane containing A, B, and C. NOTE: Enter the exact answer. Distance

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

A: The vector that passes through the points: Ax1, y1, z1 and Bx2, y2, z2 is defined as…

Q: (0,1,1) to the line of intersection of the planes : x + 2y + z = 1 x - y + 2z = -8

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Q: Show that the line [x, y, z]= [5,-1,3]+[4,-5,2] lies on the planes 3x+2y-z = 10 and 7x+4y-4z=19.

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Q: Find a plane through P (2, 1, 1) and perpendicular to the line of intersec- tion of the planes:…

A: find a plane through P2,1,1 and perpendicular to the line of intersection of the planes  2x+y-z=3 ,…

Q: Find the distance from y to the plane in R spanned by the set {u1, uz} 4 - 3 -3 y = -9 -4 Uz 2 4 1…

A: Solution   Given,       Find the distance from  γ to the plane  in R3       spanned  by the  set…

Q: Which point(s) lie in the plane 2x + y - z = 10? a) (0, 0, 10) c) (2, 4, - 2) b) (5, 3, - 3) d) (-3,…

A: Given:plane: 2x+y-z=10

Q: Let A = and B = , P = (9, 8, 7) e. Find the volume of the parallelepiped spanned by A, B, and P…

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Q: ● Let u = 2-25 - 2k + ● and = 2î - 2Ĵ+k. Find a vector w such that the parallelepiped spanned by u,…

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Q: 3) Find the distances: a. Between ₁ = (3 + t, −2+ 3t, -t) and 1₂ = (1 + 2t, t, 5+ 4t). b. Between…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

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: Determine a so that the line x-3/a=y+5/2=z+1/4 is parallel to the plane 2x+3y-5z=14.

A: To determine  so that the line  is parallel to the plane .

Q: Please state what each and every variable  joins to do a, b, c or d . Please do it for all parts e.g…

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Q: Find the distance from y to the plane in R³ spanned by the set (U₁, U₂} 6 - 2 4 y = -9 a. b. C. 43₁…

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Q: Consider the points A(3, –3, 5), B(5, –5, 2), C(-1, –4, 2), and D(4, 1, –8). (a) Find the volume of…

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