Consider the points A(2, –3, 4), B(4, –5, 1), C'(-2, –4, 1), and D(4, 2, –6). (a) Find the volume of the parallelepiped that has the vectors AB, AC, and AĎ as adjacent edges. NOTE: Enter the exact answer. Volume =| (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: The plane 7= [1,0,0]+t[1,1,1]+s[L,−1,1]; s,t €R contains the point (3,0, p). Find the value of p.

A: Given r=(1,0,0)+t(1,1,1)+s(1,-1,1)

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: 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: Let u = 4 h = V= and w= 1 . For what value of h is w in the plane spanned by u am

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Q: Find the point on the plane x+y+z=-46 that is closest to the point (1,1,1).

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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: 2x+y 5x+6y Find [/02/53 -dA, where R is the parallelogram enclosed by the lines R 2x+y=0, 2x+y=9,…

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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: 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…

A:

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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