Q1) consider a plain (M) that contains the three points A(1,-1,1), B(2,3,0), and C(0,1,-2) a Find the equation of the plane b. Find the parametric equations of the line through the point P(1,0,-2) and perpendicular to the plain. c. find the closest point on the plane to the point P(2,2,2)

Q: Given the points A(7, -2, -9 ) and B( 7, −2, 2 ). Question 3 a) [:] Write parametric and symmetric…

A: We have to find the equation of line and intersection of line and plane.

Q: The line ℓ is given by the equations x −2y + z = 2 and x + y −3z = 4. That is, ℓ consists of all…

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Q: Find an equation of the plane pirpendicular to the line through (2,2,-4) and (9, "1, 3) and…

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Q: Where does the line with parametric equations −1+3t y = 2 - 2t 2 = 3+ t intersect the plane 3x + y -…

A: Given parametric equation of line x = -1 + 3t y = 2 - 2t z = 3 + t Given plane 3x + y - 4z = -4

Q: 91 a) Find an equation of the sphere with center (1,-3,-5) and tangent to xz-plane.

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Q: How do you find the parametric and symmetric equation of the line passing through the point (3, 2,…

A: We have to find the parametric and symmetric form of the line perpendicular to the given plane at a…

Q: Determine parametric equations of the line of intersection of the planes x+2y+3z=4 and -2x+z=0. Then…

A: Let us consider two planes ax+by+cz+d=0 and a'x+b'y+c'z+d'=0  Intersection of two planes is line…

Q: Consider the Point (-2,1,3) and the plane -3x2 +x2 +4x3=7. Find parametric equations of the line…

A: The direction vector of a line perpendicular to a plane is same as the normal vector of the…

Q: Find a parametric equation for the line through the point (2,3, – 1) and perpendicular to the plane…

A: Given that The point on the line (2,3,-1) and perpendicular to the plane 8x+3y+3z=5 A vector…

Q: Find parametric equations for the line through Po = (10,-1, 1) perpendicular to the plane 2x + 3y -…

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Q: 2. Determine parametric equations of the line that.... 4 a) passes through (-9,8) with slope - 5 b)…

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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.