Problem 2. The plane z = az + by + c is said to be best-fitted to the data points (1, 3₁, 21) = (0, 0, 0) (T2, J2, 22) = (0, 1, 1) (T3, y3, 23) = (1, 1, 1) (x4, 9₁, z4) = (1, 0,-1) provided the values a, b, and c minimize the function 4 f(a,b,c) = [ (axi + byi + c - zi) ². i=1 This function represents the sum of the squares of the vertical displacements of the of the data points (Ti, Ji, Zi) from the plane z = ax + by + c. Solve this problem for a, b, and c.

Q: 6. Determine if the vectors vị = (1, -1,3, –1), v2 = (1, –1, 4, 2), v3 = (1, -1,5, 7) dependent or…

A: We have to find that given vectors are linearly dependent  or linearly independent.

Q: Find the equation of the plane that contains the line x = 1+t, y = 2+2t, z = 3- (1, -2,4). e point p…

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Q: Suppose that Mrs. Jena (in the position of T) want to travel to the top of regions diagonally right…

A: To find the number of route to reach the top of the region :-

Q: The Cartesian equations of the line perpendicular to the plane 2x -3y + 4z + 8=0 and passing:…

A:

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: If I is a line passing through the point (1, 2, 3) and perpendicular to the plane 2r+3y-== 5, which…

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Q: Let L7 be the line passing through the points Q1=(3,-5, –1) and Q2=(0, 4, –10). Find a value of k so…

A: Given that L1 be the passing through the points Q1=(3,-5,-1) and Q2=(0,4,-10). And the line  L2 be…

Q: Find the intersection of the line x = -1 + 2t, y = 3 + t, z = 4 - t with the yz-plane. O (1, -3, -4)…

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Q: 10. Find an equation of the plane that passes through the points (x, y, z) = (1, 2, −1), (x, y, z) =…

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Find the equation of the planes that contains two lines given by L₁: x= 1-2t, y = 4 + t, z = t and O…

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Q: 11. Given đ = (2, x, –3) and b = (5,–10,y), for what values of x and y are the vectors collinear?

A: We have to find the values of x and y for which bothe the vectors are colinear

Q: x² = y² + 4z²

A: I am solving first one question due to guidelines.Since given surface is  x2-y2+4z2 ≡f(x,y,z)=0that…

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: Let Lz be the line passing through the points Q1=(1, 3, 1) and Q2=(7, 12, 4). Find a value of k so…

A: We will solve the problem