Find the distance from (.-4,5) to each of the following. (a) the xy-plane (b) the yz-plane (c) the xz-plane

Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: Find the distance from the point (2, 2, 3) to the plane 2x + 3y + 5z = 0.

A: Formula of distance of a point from a plane:

Q: Which point(s) lie in the plane 2x + y - z = 10? a) (0, 0, 10) c) (2, 4, - 2) b) (5, 3, - 3) d) (-3,…

A: Given:plane: 2x+y-z=10

Q: Find the cosine of the angle between the planes -3x - 4y – 3z = 3 and the plane - 1x - 3y + 3z = -2.

A:

Q: Find the angle between the lines y-V3x-5=0 and 3y-x+6=0. %3D

A:

Q: nterseeting Lines Finad the plane determined by the Loi Xi=l-2t, , J="l-st,, 2= -2+t, L2: X2=-3+t2,…

A:

Q: Describe the plane x = 4.

A: Given, plane x=4we have to describe the plane x=4

Q: Write the equation of the locus of a point whose distance from the plane 3x-2y-6z=12 is always twic…

A: We have to find the locus of the point P with the relation as per the distances given.

Q: Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, - 1).

A: We have to find a direction vector for the line containing the points -1, 5, 2 and 2, 3, -1. We know…

Q: Determine the parametric and symmetric equations for the line through the given points (2, –7,5),…

A:

Q: Show that the points (5,4,2),(6,2,-1) and (8,-2,-7) are collinear

A: The points are A(5, 4, 2), B(6, 2, -1) and C(8, -2, -7) The points are collinear if the directional…

Q: Find Sax ds, where C is the line segment in the plane joining (0,0) and (3, 4).

A: I am attaching image so that you understand each and every step.

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.