Find a number a so that the change of coordinates s = x + ay, t = y transforms the integral ff dady over the parallelogram R in the xy-plane into an integral S a(x, y) a(s, t) over a rectangle T in the s-t plane, where the parallelogram R has vertices (0, 0), (10, 0), (-15, 5), (-5,5 dsdt

Q: Find the plane that gives the best fit to the 4 values b = (0, 1, 3, 4) at the corners (1, 0) and…

A: In this problem, we are looking to find the plane that gives the best fit to the 4 points (1, 0),…

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

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 scalar equation for the plane passing through the point P=(−5, 3, 2) and containing the…

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Q: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.

A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…

Q: Let 5x + 3y + 10% = 0 be the equation of the 3 plane in R³ spanned by (1, a, 0) and (1,0, b). Find…

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Q: Let the solid form in the orthogonal coordinate system xyz be surrounded by points A, B, C, D and F,…

A: The given co-ordinates of vertices are A = (-4, 1, 3), B = (6, 1, 1), C = ( 9, 5, 0), D = (4, 5, 1),…

Q: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

A: We know that equation of line passing through the points (x1,y1,z1) and (x2,y2,z2) is

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: 1) m/00 Adding Prop +-0

A: Given that 38+14=38+14*2238+14=38+2838+14=3+2838+14=58 The answer is 5/8.

Q: Find the distance between the parallel planes 4x – 3y + 12z = 12 and 4x — Зу + 12z 36.

A: In this problem we have to find distance between two parallel planes.

Q: Find an equation for the plane through P(1,4,4) that contains the line of intersection of the planes…

A: Let the equation of the plane that contains the line of intersection of the planes 3x-y+3z=-1 and…

Q: Find the distance between two lines (L1: x=3t-1, y=t+6, z=2t+3 and L2: x=2t+6, y=2t+11, z=-t+3)…

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Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

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Q: Calculate the cross product assuming that u X w = (-2, -3, -2) (2u + 4w) × w = {

A: Given u × w = -2, -3, -2