(A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 If the plane meet with the line x-+2t, y -2t and z 1+t?

Q: Find the equation of the plane that contains the line x = 1+t, y = 2+2t, z = 3- (1, -2,4). e point p…

A:

Q: Find the shortest distance between the line L1:2x + y - 3 = 0 and the plane P1:3x - 4y + 12z + 5 =…

A: The formula for the distance between a point and a plane must be used to determine the shortest…

Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: is the line x = 1 - 2t, y = 2 + 5t, z =-3t parallel to the plane 2x + y - z = 8? Give reasons for…

A: Given,

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: Determine a so that the line x-3/a=y+5/2=z+1/4 is parallel to the plane 2x+3y-5z=14.

A: To determine  so that the line  is parallel to the plane .

Q: Find equations for the line perpendicular to the plane x + 5y - 2z = 6 and through the point of…

A:

Q: Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = 0. -000…

A: The objective of this question is to find the point of intersection between a given line and a…

Q: 17. Find the intercepts of the plane 2x + 6y − 3z - 12 = 0. -

A: Intercepts are : 6, 2, -4Explanation:

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.