(31) Find a plane through A(2, 1, –1) and perpendicular to the line of intersection of the planes 2x + y-z=3 and x + 2y +z=2.

Q: (vi) Find an equation of the plane that passes through the line of intersection of the planes x – z…

A:

Q: find the equation of the plane through P(1, 3, 2) that is parallel to the plane 5x - 4y + 3z = 7

A:

Q: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

A:

Q: 1) Consider the two planes x 2y + z = -5 and 3x 2y - z = 1 (a) Find an equation for the line of…

A: The solution is given as follows

Q: Find the intersection of the line r(t) = 3t + 2, 1, −7t and the plane 2x − 3y + z = 5.

A: r(t)=3t+2, 1, -7t and the plane 2x-3y+z=5

Q: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

A:

Q: (222) Determine the x-, y- and z-intercepts of the plane 3x-8y-8z +24=0

A:

Q: 2) Find the point of intersection of the plane x - 5y + 3z = -127 and the line r(t) = (-2,-8, 7)t +…

A:

Q: (1) Find an equation of a plane that goes through (-1,2,6) and is perpendicular to (2, 1, –3).

A: It is given that the perpendicular vector to the plane is given as,  and plane passing through,…

Q: Find an equation of the plane that passes through the line of intersection of the planes ( x – z = 1…

A: We have found the plane that passes through the line of intersection of the planes x-z=1 &…

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.