Just like in a projective plane, two distinct lines always intersect on the spherical plane.

Q: Find parametric equations for the line in which the planes, x+2y-2z=5 and 5x-2y-z=0 intersects. Show…

A: Given, The equation of intersecting planes, x+2y-2z=5 and 5x-2y-z=0.   We have, x + 2y = 2z + 5 and…

Q: Find an equation of a plane making an angle of π/2 with the plane 3x + y − 4z = 2

A: Here we have to find the equation of plane  making an angle of π/2 with the plane 3x + y − 4z = 2

Q: What is the distance from the point P=(2, -1, 4) to the plane 3x+5y-2z =20

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Q: Explain why in spherical coordinates the graph of = c is a half-plane and not an entire plane.

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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: Can two horizontal planes intersect?

A: Explanation: If two planes are horizontal, it means both are parallel to the x-axis.

Q: Find the parametric equations for the line in which the planes x-2y+4z=2 and x+2y-2z=6 intersects

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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 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: What is plane and cartesian plane?

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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: he intercepts of the plane given by

A: Intercepts of the plane are (3,5,3).

Q: Do two points determine a plane?

A: No.

Q: Through the point (2, -4, 0) and parallel to each of the planes 2x + y -z = 0 and x+ 5y + 3z = 0.

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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…

Q: Find the equation for the plane that passes through (2,4,-1) and contains the intersection of the…

A: The plane equation Ax+By+Cz+D=0 passing through three points x1,y1,z1, x2,y2,z2 and x3,y3,z3 is…