What point on the sphere is closest to the plane?

Q: Consider the planes given by the equations x + 2y + 3z = 4 3x + 4y + 5z = 2 5x + 4y + (k - 1)z = k –…

A: This is a non homogeneous system AX=b Concepts required : Infinite solution of the system AX=b will…

Q: 4. Find the perimeter of the figure on the coordinate plane. 4 M(0, 4) L(-3, 0) N(3, 0) -4 2, 4. -2…

A: We have to find the parameter of the given figure.

Q: Explain why it is impossible to find four points on the same plane equidistant from each other.

A: Let us imagine that we have 3 points in a plane that are equidistant from each other. These points…

Q: Sketch and identify the graph of z² = x² + You may either sketch the traces onto the xy-, xz- and…

A: The given equation is z2=x2+y24. To Find: The sketch of the given equation. The given equation have…

Q: 3. Find a rectangular equation to represent the plane curve. x = 3 tant, y = 2 sect for tin (-7-7)

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Q: Name two planes that intersect in FG.

A: We have to name the plane which intersects in FG,

Q: A glass sphere given by the equation (x-1)²+(y-2)²+(-3)² = 36 is floating above the plane 2x + y -…

A: The given problem is to find the point on given sphere is farthest from the given plane. Given…

Q: Find the equation of the XZ plane.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the standard equation of the sphere. (Let r = 5 and C = (9, 7, 5).)

A: Standard equation of a sphere with radius r and centre at c=(h,k,l) is  (x-h)2+(y-k)2+(z-l)2=r2

Q: Find an equation of the plane

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Q: ind the distance between the point (-1, 2, 1) and the plane 2x + 3y - 4z = 7. OTE: Give your answer…

A: Given query is to find the distance between the point and the plane.

Q: 9. Plot these three coordinate points on the given Cartesian Plane: (2,3) (-2,1) (4,-1) Join the…

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Q: Determine the scaler equation of a plane that contains the point (3, 1, -2) and Y-axis.

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Q: i) x² + 25 y² – 4x + 100y +4 = 0 - ii) x² – y2 – 6x = 0.

A: i) Given equation, x2+25y2-4x+100y+4=0 Now…

Q: x = 1 + 2t, y = 4t, z = 23t; x+2yz + 1 = 0

A:

Q: Find the distance of the plane passing through the points ā, b, c from the origin.

A: First we derive the vector equation of plane.    The perpendicular distance is the projection on the…