Find the distance between the point (0,0,0) and the plane 2x – y + 2z = 4

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: Find the points on the surface 1x? + 3y2 + 5z2 = 1 at which the tangent plane is parallel to the…

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Q: Find the equation of the plane tangent to the surface G(x,y, z) = 2x² - y² – 3z2 = -4 at P = (-2,…

A: Given surface is                                                G(x, y, z): 2x2-y2-3z2=-4 we have to…

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: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = √(y - x),…

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Q: Find a formula for the distance from the point P(x, y, z) to the yz-plane.

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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: z = In (x² + y²) at point Po(1,0, 0).

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Q: Find the distance between the skew lines with parametric equations x 2 + t, y = 1 + 6t, z = 2t, and…

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

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Q: Find an equation for the plane that is tangent to the surface z = In (x³ + y²) at the point…

A: Given:   A surface   z = ln x3 + y2   To Find :  An equation  for the plane that is tangent to the…

Q: 2. Find the equation of the plane tangent to the elliptic paraboloid z = point (1, 1,3). 2.a2 +y, at…

A: To find out the equation of the plane tangent to the elliptic paraboloid.

Q: Find an equation for the plane that is tangent to the surface z = In (x´ +y) at the point P(1,0,0).…

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Q: Find parametric equations for the intersection of the planes 2x + y − 3z = 0 and x + y = 1

A: Two planes lying in 3-Dimensional plane can intersect each other at any point and that point can lie…

Q: Find the shortest distance between the surface z = x² + y² and the plane r + y – z = 4.

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Q: Find a parametrization of the line in which the planes x+y +z= -2 and y +z= 6 intersect.

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Q: Find all points on the ellipsoid 2x² + 3y² + 4z² = 9at which the plane tangent to the ellipsoid is…

A: Explanation: Given that,  Ellipsoid:2x2+3y2+4z2=9Plane:x-2y+3z=5⇒15x-25y+35z=1   Suppose point of…

Q: Find a parametric equation for the curve of intersection of the cone x²+y² = z² and the plane x+2z =…

A: We have to find a parametric equation for the curve of intersection of the cone x2+y2=z2 and the…

Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: Find an equation of the surface consisting of all points P(x, y, z) that are twice as far from the…

A: Let d1 be the distance from the point 0,0,1 to the point Px,y,z and d2 be the distance from the…

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 for the plane that is tangent to the surface z In (x +y) at the point P(0,1,0).…

A: By using partial derivatives and tangent equation to surface

Q: the trace of the surface in the plane x=1?

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: Find an equation for the plane that is tangent to the surface z= In (x* +y) at the point P(1,0,0).…

A: The solution for the above question is as shown below.

Q: Find the angle between the two planes −2x + y + z = 2,  6x − 3y + 2z = 4 and find a set of…

A: The given planes are −2x + y + z = 2  and  6x − 3y + 2z = 4 . Obtain the angle between them as…

Q: V7x + 2y – x = y.

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Q: Find the distance between the skew lines with parametric equations  x = 1 + t, y = 3 + 6t, z = 2t,…

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Q: Find the distance from the point S(0,0,0) to the plane 20x+10y+5z=70 (approxmate to two decimal…

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Q: Find the equation oftangent plane and normal lines of the surface: ƒ(x, y, z) = 10x² –14 y² +11z³-7…

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Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: Find the parametric equation of the line of intersection of two planes correctly: P1:x+3y+5z=0 and…

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Q: Find an equation for the plane that is tangent to the surface z = In (x+y) at the point P(0,1,0).…

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Q: Find parametric equations for the line pass- ng through the point P(1, –1, 3) and perpen- licular to…

A: Given that: Line is passing through P(1,-1,3) and perpendicular to the plane:       4x+3y-2z=6.

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: 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 parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

Q: Determine the equation of a plane parallel to x-z plane which is tangent to the circle…

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Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

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Q: Find the distance between two planes a and a1 that are tangent to the ellipsoid 2 +2y? + z² = 5/8…

A: We have to find the distance between the two tangent planes parallel to x+y+z=0  that are tangent to…

Q: Find the equation of the plane tangent to the surface z x+y at the point (2, 1, 3). x-1

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Q: Find equations of the Normal plane and Osculating plane of the y = 2t, x = 2 sin 3t , z = -2cos 3t…

A: Given vector rt=2sin3t,2t,-2cos3t. Then r't=6cos3t,2,6sin3t. The given point is 0,π,-2. Now the…

Q: Find the surface area of the part of the plane 3x + 3y+ z = 9 that lies above the triangle formed by…

A: In the question we have to find the surface area of the plane.

Q: Find an equation of the plane tangent to the surface z2 - xy = 14 at (2, 1, 4).

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Q: Find the plane tangent to the surface z=x+ y at the point (3,4,25). a. 6x+8y-z=25 b. 6x-8y-z=25 c.…

A: We have to find the plane tangent for the given surface

Q: Find the point at which the line with parametric equations x = 3 + 4t, y = 5 – 2t, z = 4 + 7t…

A: According to question,Given equation of line in parametric form,x = 3+4t,y = 5-2t,z= 4 +7t,Equation…

Q: Find the equation of the line tangent to the intersection of the surface z = arctan ry with the…

A: The tangent line to a plane curve at a particular position is the straight line that "just touches"…

Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

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Q: Find the parametric equation of the line of intersection of the planes 2x+y-z=1 and x-2y+3z-9

A: First find cross product take normal vector useformula

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.