Apply T (x, y) = (2x/3,2y/3) to the following pentagons: (a) vertices (3,-3), (3, 3), (0, 6), (–3, 3), and (-3,-3); (b) vertices (15, 0), (15, 6), (12, 9), (9, 6), and (9, 0). Are the results what you expected? %3D

Q: Find the point on the plane x+5y+2z=14 closest to the point​ (1,1,1).

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Q: Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

A: Given : The equation of the planes are x+ 2y + 6z = 1 and x + 2y + 6z = 10 .

Q: Find the distance between these two planes x + .2y – 2z = 3 and 2x + 4y – 4z = 7 اخترأحد الخيارات а.…

A: Given: x+2y-2z=3                                                          ..12x+4y-4z=7…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0, 1, 1).

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Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

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Q: Find the point on the plane x + 2y + 3z = 13 closest to the point (1, 1, 1).

A: Given plane is We need to find the point on the plane closest to

Q: Find the point(s) on the plane 4x +3y +z = 2 that are closest to (1,-1,1).

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Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: Find the intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

Q: Find the point on the plane x-y+z=7 that is closest to the point (2,4,6).

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Q: F = (-3y, 3x); R is the triangle with vertices (0, 0), (1, 0), and (0, 2).

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Q: Find the line of intersection of the planes 3x+2y-z=7 and x-4y+2z=0.

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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: 5) Find the distances: a. Between l, = (2 + 2t, –1+ t,–3t) and l, = (4,–5 – 3t, 1+ 4t). %3D b.…

A: Given: (a). two lines l1 and l2 (b). Two Planes (c). A point (1,2,3) and a line  To Find: (a).…

Q: Find the equation of the plane through the point (1,2,-1) and parallel to the plane 2x- 3y+4z+6-D0.…

A: To find: The equation of plane passing through the point 1,2,-1 and parallel to plane 2x-3y+4z+6=0.…

Q: Find the distance between the planes 5x - 3y + z = 9 and 5x 3y + z = -2.

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Q: Find the distance between the planes 5x - 3y + z = 9 and 5x - 3y + z = -6.

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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: Find the distance between these two planes x + 2y –' 2z = 3 and 2x + 4y - 4z = 7.

A: Devide the equation of 2nd plane by 2 .we get that both planes are parallel so just apply formula…

Q: (x² +2y) where D is the triangular region with vertices (0, 1), (1,2) and (4,1).

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Q: Find a vector parallel to the line of intersection of the planes 2x + y - 3z =13 and x + 3y + 5z =-8

A: Given, The equation of the planes  2x+y-3z=13 x+3y+5z=-8 We have to find a vector parallel to the…

Q: Find all planes in R3 whose intersection with the xz-plane is theline with equation 3x + 2z = 5.

A: Find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

Q: Find the point on the plane 3x + 4y +z = 8 that is nearest to (2,0,1).

A: Given the equation of plane:

Q: Find the point on the plane 4x+7y+8z−19=0 closest to the point (−2​,1​,3​).

A: Given,

Q: Find the angles between the planes 5x + y - z = 10, x - 2y + 3z = -1

A: Solution -  We have equation of two planes -  Plane 1 -…

Q: Find all planes in R^3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

A: To find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.…

Q: Find the angle (in degrees) between the planes 4y + z = 4 and – 4x + 2z= - 3.

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Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0.

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Q: Use the Lagrange multiplier method to find the point on the plane 4x +3y +2z = 0 with the smallest…

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Q: Find the line of intersection of the given planes. 3x + 2y + z = ~ 1 and 2x - y + 4z = 5

A: Given: 3x+2y+z=−1                                                      ...(i)2x−y+4z=5…

Q: Find the distance between the planes. 5x-2y+z-4 0, 5x-2y+z+6= 0

A: Given,  Equation of Plane 1: 5x - 2y + z - 4 = 0 Equation of Plane 2: 5x - 2y +z + 6 = 0 From the…

Q: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

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Q: Find the point on the plane 2x + 3y + z = 7 that is nearest to​ (2,0,1).

A: NOTE: Refresh your page if you can't see any equations. . the given point is . the given plane is…

Q: Compute the angle between the two planes 2x + 3y + 7z = 2 and 4x - 2y + 2z = 4.

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Q: A point moves in the (x, y) plane on the line 2x+ 3y −4 = 0. Where will it be when the sum of the…

A: We have to find a point from where the sum of square of its distances from 1,0 and -1,0 is smallest.

Q: Use Lagrange multipliers to find the point on the plane  x − 2y + 3z = 6  that is closest to the…

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Q: 2. Trapezoid QRST with vertices Q(3. 1), R(5, 2), S(10, 0), and T(4, -3); 270° counterclockwise…

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Q: Find the point on the plane 4x+5y+x=11 that is nearest to (2,0,1). What are the values for x, y, and…

A: The equation of the plane is

Q: 4. Use the method of Lagrange Multipliers to find the point on the plane r+y- 2 = 5 that is closest…

A: Given: The plane equation is x+y-z=5 and the point is -3, 5, 4.

Q: Find the line of intersection of the planes 2x – y + z = 2 and x + 2y – 4z = 1

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Q: Find the symmetric equations of the L that is parallel to the two planes x + 2y - z= 2 and x + 6y+ z…

A: Given: Two planes, P1: x+2y-z=2, P2: x+6y+z=-3, Point P1, 2, 3

Q: find the line of intersection of th e given planes. 3x + 2y + z = -1 and 2x - y + 4z = 5

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Q: the

A: We will find the distance.

Q: Find the distance between the planes 4x + 6y – 2z = 4 and –2x – 3y + z = -3.

A: We have to find out the distance between two planes

Q: Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y - z = 0.

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Q: Find the distance from S(1, 1, 3) to the plane 3x + 2y + 6z = 6.

A: It is given that a point S1, 1, 3 and the equation of the plane 3x+2y+6z=6   Here x1=1, y1=1, z1=3…

Q: Find the distances (a) Between l1 = (2+ 2t, –1+t, -3t) and l2 = (4, -5 – 3t, 1+ 4t) (b) Between the…

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Q: Find the point on the circle x2 + y2 = 1 that is closest to the point (1, 3/4) by using the method…

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Q: 1. F = [2², -x², 0], S the rectangle with vertices (0, 0, 0), (1, 0, 0), (0, 4, 4), (1, 4, 4)

A: As given that,  F→=z2i^-x2j^+0k^ Calculating curl F,…

Q: Find the distance between the point Q (3, –2, 4) and the plane 2x – 5y + z = 10 -

A: