B A F G E Figure 1

Q: What is the distance of the origin to the plane through (√3, √3,0), (√3,0, √3) and (0,√3,√3).

A: We have to find the distance of the origin to the plane passing through  and .

Q: Let Z = (1, 1, 2) be a point in R³. Find the closest point to Z tha lies on the plane give by -x+y-z…

A: The normal vector to the plane is <-1, 1, -1>. The point you seek would have to be some…

Q: Consider the simple linear model Y; = Bo + B1Xi + €¿, where e~N(0,0²); i = 1,2, .. 1. Show that a)…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts(a, b-i,…

Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

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Q: Q10) Find the equation of the plane passing through the point P(1,-1,2) and parallel to the line x-1…

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Q: If (x, y) and (X, Y) are the coordinates of the same point referred to two sets of rectangular axes…

A: and are the co-ordinates of the same point referred to the set of rectangular axes with same origin.

Q: Evaluate SdV where G is enclosed by the paraboloids z = G z = 4 x² - y². Answer: 2π 3x² + 3y² and

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Q: Transform (0, 5, 2) from rectangular into spherical form (here z is any negative number).

A: given rectangular coordinates is of the form (x, y, z) are (0,5,z) Now we are going to find…

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: ind the equation of the tongent plane to fox,y)=x²-2xy + 2y ² slope 2 in the positive x direction…

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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: 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: could pls solve this with all steps and in handwritten for me to better undertsand thanks  For the…

A: Given: For the system of three planes:  -4x + 3y + 2z = 2 4x - 3y - 2z = 2  2x + y - 4z = -16 To…

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: 2. Line m passes through the points (3, – 7) and (9,8). When line n is plotted, it has no points of…

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Q: Q1) the plane has equation of 4x-3y-2+5=0 Pud equation of plane partlel to R) and contimons with…

A: Given that: Equation of given plane is: 4x-3y-245=0and contains point (2,1,3)

Q: ㅠ ⑤Prove that Imz=0, larg 2 - 11 = 1, Z-Z=0, 12-il = 1Z+il are different equations all describing…

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Q: The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid

A: Solution Given The intersection gives z2=1-x2+y2we need to find the centroid

Q: Find the matrin of linear 2 22

A: The domain of the given transformation is R3:   To find the matrix of the linear transformation,…

Q: Find the point on the plane 3x - 2y + z = 16 that is closest to the point (1,2,3). (Use the method…

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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: A plane through the three points P = (4, -3, 5), Q = (-2, -3, 5), and R= (-2, 3, -3) is described by…

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Q: 4. a) Find the point on the unit sphere x² + y² + z² = 1 that is closest to (1,2,3). b) Find the…

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