Find the equations of planes that just touch the sphere (x – 4)² + (y – 5)² + (z – 2)² = 16 and are parallel to - - (a) The xy-plane: and (b) The yz-plane: and (c) The xz-plane: and

Q: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…

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Q: Find the distance from the point (3, 2, 5) to the plane whose general equation is 2x + 3y - z = 0.

A: we have to find the distance from the point (3,2,5) to the plane whose general equation is 2x+3y-z=0…

Q: fficients of x, y, and z in the given equation of the plane. ..... z= -7+ 9t. pe expressions using t…

A: Find parametric equation.

Q: 2. The plane containing the point (-8, 3, 7) and parallel to the plane given by 4x+8y-2z=45.

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Q: Find parametric equations for the line of intersection of the planes x + 2y + 3z = 4 and 5x + 6y +…

A: Given: x+2y+3z=4   and  5x+6y+7z=8To obtain the parrametric…

Q: Find the standard equation of the sphere with center (−3, 2, 4) that is tangent to the plane given…

A: Radius (r) will be the distance from the center to the tangent plane. That is the distance between…

Q: 6. Determine the distance from the point (2, -1, 5) to the plane 3x - 3y + 5z = 8.

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Q: Find the standard equation of the sphere with center (-4, 3, 8) that is tangent to the plane given…

A: The center of the sphere is (-4,3,8) . The tangent plane is 3x+8y-4z=24 The radius of the sphere is…

Q: Determine the equation of the plane containing the points (3, 1, 4) and (2,7, 1) and is perpen-…

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Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

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Q: Find an equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the point…

A: To find the equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the…

Q: 5z' + 3z gral z² - 4 plane, is

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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 general equation of the plane spanned by

A: Given vectors are 111 and 321

Q: Find all point cs) 2= 8- 3x2- 2y2 マh where the fameyent plane orlhugana l i's to とk 2ihe. X 2-31,…

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Q: 4. Give the general equation of the plane containing the point (3,-1,4) and 2- z perpendicular to…

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Q: find the distance from the point to the plane. (0, 0, 0), 3x + 2y + 6z = 6

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Q: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

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Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: 3. Among all the points on the graph of z = 10 – x² – y² above the plane x + 2y + 3z = 0, find the…

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: 37 Find the equaton of a plane that contains the point (4, -3, –1) and is perpendicular to the…

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Q: 7. Find the distance between the point (- 3, 2, 1) and the plane with equation x - 2y + 3z = 5

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Q: Find the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…

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Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: Find an equation for the plane through the point (3, 4, −4) and parallel to the plane defined by 4x…

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Q: Find an equation of a plane passing through the points (1, –1, 7), (3, 2, –20) and perpendicular to…

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Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: 7. Find the distance between the point (3, 1, –2) and the plane x + 2y – 2z = 4.

A: Given that plane x+2y-2z=4 and point 3,1,-2To find :Distance between point and plane Solution if…

Q: Find the distance between the point (2, 0, 1) and the plane 2x - 3y + 6z = 6.

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Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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Q: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x + y – 2z…

A: Given:

Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane - 6x + 8y – 10z - 4 = 0 are in…

A: We find out the results by using vectors in 3D

Q: Give the general equation of the plane satisfying the given condition. plane Σ containing the point…

A: We will find the equation of the plane Σ which is parallel to the plain 2x − 6y + 3z = 0 and…

Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

Q: Find a scalar equation of the plane that contains the linex = 1 + t, y = 2 − t, z = 4 − 3tand is…

A: Given,The plane that contains the line x = 1 + t, y = 2 − t, z = 4 − 3t.So, we can say that the…

Q: 5. Calculate the distance between the point (3, 1, -2) and the plane 2x + y-2+1. O 10 o -10 V14 O 10…

A: The equation of the plane is  2x+y-z+1 = 0 The point is x0,y0,z0 =3,1,-2 To evaluate : The distance…

Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: Find the standard equation of the sphere with center (-6, 2, 7) that is tangent to the plane given…

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Q: Find the equation of the xy-trace of the sphere. (x + 2)2 + (y + 1)2 + (z − 3)2 = 25

A: The equation of the sphere: - The general equation of a sphere is (x – a)2+(y-b)2+(z-c)2=r2 if (a,…

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

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Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+y-2z = 3.

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Q: 12. Find the distance between the point (3,-2,7) and the plane 4x – 6 y + z = 5.

A: The equation of plane is 4x-6y+z=5 and the given point is 3,-2,7. The distance between the point and…

Q: Find the distance from the point (5, 4, 3) to the plane −4x−1y−1z=4.

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Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…

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Q: Find the equations of planes that just touch the sphere (x−5)^2+(y−3)^2+(z−1)^2=9 and are parallel…

A: Solution  Given (x−5)^2+(y−3)^2+(z−1)^2=9 (a)  Parallel to the  xy-plane:   ( z-1)2= 9   z - 1= | 3…

Q: Give an equation of the plane whose trace in the yz-plane has equation y = 6z, and in the xy-plane…

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Q: 3. Find the equation of the plane parallel to the plane with equation 18x + 6y – 5z = 0 and passing…

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Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane – 6x + 8y – 10z 4 = 0 are in…

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