Analytic Geometry Answers

Let R be the point which divides the line segment joining P(2,1,0) and Q(−1,3,4) into the ratio 1 : 2 such that PR < PQ. Find the equation of the line passing through R and parallel to the line

(x /2) = y = (z/ 2)

Find the equation of the normal of the paraboloid 3x² +4z² + 4y = 0 at the point (2,−4,1). Also find the point where this line again intersects the paraboloid.

Find the equation of the cylinder with base

x² + y² + z² + 3x+ 3y−z = 1,x + y+ 2z = 2.

please solve ASAP. :(

Find the equation of the plane which passes through the line of intersection of the planes x+y−2z = 1 and 2x+y−4z = 3 and which is perpendicular to the plane x+y+z = 1

Find the equation of the tangent plane to the conicoid x² +y² = kz at the point (k, k,2k), where k is a constant. Represent the plane geometrically. Now take different values of k, including both positive and negative, and see how the shape of the conicoid changes.

please solve ASAP:(

Find the distance of the point of intersection of the line

(x-2/1) = (y+3/-1) = z/3

and the plane 2x- 3y +4z+ 4=0 from the origin.

Given that P = (8, 8) and Q = (9, 17), find the component form and magnitude of the vector PQ.

1. X-2/2=y-3/-1=z+4/3
2. X-3=y+1/3=z-1/-2

Find the equation of plane which containing the two lines

Assume that U is a plane.

Find out whether or not the following vectors lie in U:

(10.1) ~u =< 3.8, 1 >, ~v =< −4, 1, 1 > and w~ = −~v

(10.2) ~u =< 3.8, 1 >, ~v =< −4, 1, 1 > and w~ = ~u − ~

Knowing the fact that the cross product of two vectors ~ux~v is orthogonal to both vectors ~u and ~v, find a case where this is not applicable.