f we need to find the equation of a plane when given a point in 3-dimensions and two planes that intersect in a line that is contained in the objective plane, how do we find the line of intersection of the two given planes and then proceed to find two points on that line so that we may find the equation of the objective plane with three points and the cross product (to find the normal plane)? Please do an example with point (3, 1, 4) and planes x + 2y + 3z = 1 and 2x - y + z = -3, and please explain all of the steps and use typefont. Thank you!

Q: if y = 5/2[e^x/5 + e^-x/5], the show that y,, = y/25

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Q: Find the equations of the line formed by the intersection of the planes P1= x-6y+2z=12 and…

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Q: Represent two planes that intersect at a line represented by 3. y- 7 = z+2 2.

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Q: What is the equation of a line that is perpendicular to the line y = - x-1 and passes through the…

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Q: The line whose equation is given as: (x-2z-2=0, y-22 -0) intersects the plane (x-2y+2-1-0) at the…

A: Given: x-2z-2=0 y-2z=0 equation of plane x-2y+z-1=0

Q: The plane through the points (8,-2,-5), (4,-7,5), (3,-1,8) has equation Ax+By+Cz = D. If A = -75…

A: Given: The plane through the points (8,-2,-5),(4,-7,5),(3,-1,8) hasequation Ax+By+Cz=D. We are…

Q: Three companies build towers to provide signals of mobile phones in a remote area. The map is place…

A: The standard form of a circle is: (x-h)2+(y-k)2=r2 Where,  (h,k) is the center of the circle. r is…

Q: The plane through the points (-1,-2,-2), (-5,-3,2), (-5,2,7) has equation Ax + By + Cz = D. If A = -…

A: A = -25 B = 20 C = -20 D= 25  For detail....go through the solution.... You can solve this problem…

Q: 5) Find the equation of the plane through the following point that also contains the given line. P =…

A: To find the equation of a plane through a point and parallel to a given line, we can use the…

Q: the equation of the straight line passes through A(2,5) amd B (3,4) IS

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Q: - 1 y - 1 -3 23. (2, – 1, – 3); z- 2 %3D 3 2 2

A: The general equation of plane is ax+by+cz+d=0. To find the equation of plane which passes through…

Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

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Q: The points (x, y) and (y, x) are mirror images of each other across the line y = x. Therefore, by…

A: (a) x=y2  mirror image across the line y=x is y=x2

Q: How would I find the equation of the plane that goes through the points (3,2,1), (4,4,1), and…

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Q: Find an equation of the plane passing through the points (1, -2,3), (4,5,-6), and (7,8, -3).

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Q: If the points (3 , y) is equidistant from (5 , -2) and (-1 , 4), find y

A: Given that: The point ( 3, y ) is equidistant from ( 5, -2 ) and ( -1, 4) . Denote the points by…

Q: Determine whether the two planes x-y + 2z = 1 -x-y +z = 3 are parallel or intersecting. Find their…

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Q: A rectangle is fenced off for a robot competition. The dimensions of the competition area are 35…

A: Solution:

Q: Find the equation of perpendicular bisector of the line passing through points (2,-5) to the point…

A: perpendicular bisector passes through mid point of the points and has perpendicular slope to the…

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.