Find the distance from the point (2, 1,−2) to the plane 6(x − 1) + 2(y − 3) + 3(z + 4) = 0

Q: Find the equation of the plane in the form z=c+mx+ny containing the line in the xy-plane where x=3,…

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Q: Find the point where the line x = 8/3+ 2t, y = -2t, z = 1 + t intersects the plane 3x + 2y + 6z = 6.

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Q: 2.) Find the Symmetric form of the equation of the line of in tersection of the two Planes X-Y +Z…

A: Let a, b and c be the direction ratios of the required line. Since the required line lies in both…

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

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Q: 2. Find the distance of the point A : (1,0, 2) from the plane P: 3x +y+ z = 9.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the point on the plane x − 2y + 3z = 6 that is closest to the point (4,2,0).

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

A: First we find out normal vector to the given plane than find out the point that is closed to the…

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: 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: 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: Find the point of intersection between the line x+2/6 = y - 3 = z/3 and the plane x + 2y – 4z = 0.

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Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-plane.

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Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…

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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: 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: Find the distance of point A(1,0,2) to the plane 3x+y+z=9?

A: Here we have to find the distance from the point A(1,0,2) to the plane 3x+y+z-9=0

Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

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: (A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 If the plane meet with…

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

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Q: 45. Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

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Q: Find the point closest to the origin on the curve of intersection of the plane x + y + z = 1 and the…

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Q: Find an equation of the plane containing the point (1,2,-2), and the line: x= 2t, y= 3-t, and z…

A: To find the equation of plane we need to find its normal vector. To find the normal vector, we…

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: The plane 6x + 8y + 60z = 700 intersects th of the highest and lowest points or coordinates

A: Given that the plane           6x+8y+60z=700  and the cone                            z2=x2+y2

Q: Find the point Q symmetric to the point P (1; 3; —4) with respect to the plane 3x+y-2z=0

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Q: find the trace of the plane in the given coordinate plane.  3x + 4z = −2, xy

A: To find the trace of the plane in the given coordinate plane  3x+4z=-2 --- (1) in the xy plane

Q: 4. Write the equation of the plane parallel to the z-axis, with xy-trace x + y - 2 = 0.

A: Write the equation of the plane parallel to z axis, with xy trace x+y-2=0.

Q: Find the point p(x, y, z) on the plane 2x + y - z - 5 = 0 that is closest to the origin.

A: Given:The given plane is 2x+y-z-5=0 that is closest to the origin.To find:we have to find…

Q: The distance from the point P(1,2,3) to the plane x +y + z = 0 is

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Q: Find the distance between the point (0, 0, 0) and the plane 2x + 3y + z = 12.

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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: Find for the point P(x,y,z) on the plane 3x + y – z – 15 = 0 that is closest to the origin.

A: The distance of the point P(x,y,z) from the origin is: d2=x2+y2+z2 Now we have to minimize d if the…

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: Find the point on the curve of intersection of the paraboloid x² • y² + 2z=4 and the plane x-y+ 2z…

A: This question can be solved by options because we have only two equations and three variables.

Q: Find the area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x =…

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Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

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Q: Find the distance from the point (1, 1, 1) to the plane 2x + 2y + z = 0.

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Q: Find the distance between the two parallel planes 5x – 3y + z – 2 = 0 %3D -10x + 6y – 2z + 3 = 0

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Q: Find the points on the hyperboloid 9x^2  - 45y^2 + 5z^2 = 45 where the tangent plane is parallel to…

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Q: Find the point on the plane 3x + 2y + z = 6 that is nearest the origin.

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Q: Find an equation of the plane that passes through the point (1,1,2) and contains the line x=3t, y=1,…

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Q: A) Find the point at which the line x = 2, y = 3+2t, z = -2- 2t meets the plane 6x + 3y - 4z = -12

A: The line is given by:x=2, y=3+2t, z=-2-2tand the plane is given by6x+3y-4z=-12.We need to find the…

Q: Find the point closest to the origin on the curve of intersection of the plane 2y + 4z = 5 and the…

A: We have to find the point closest to the origin on the curve of the intersection of the plane…

Q: Find the point on the plane x+y+z%3D24 that is closest to the point (1,1,1).

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Q: Find the point on the plane x – 3 y – 2 z = 14 that is closest to the point (0, 3, 3) .

A: We have the plane x-3y-2z=14 The normal vector to a plane ax+by+cz=d is a,b,c Hence, the normal…

Q: Find the point lying on the intersection of the plane x + + z = 0 and the sphere x2 + y2 + z2 = 25…

A: According to the given information, it is required to find a point lying on the intersection of the…

Q: Find the equation of the plane in the form z = c + mx + my containing the line in the xy-plane where…

A: Plane