Analytic Geometry Answers

The set of points M of the plane such that MA²-MB²=0 is?

A. The point I mil[AB]

B. The circle of the center I and radius [AB]

C. The null set

In the cartesian plane OXY, we consider the lines with equations

ax+3y+4=0 and x+2ay+7=0 with a as real parameter. Which of the following statements is correct?

A. There exist a unique value of a for which the lines are parallel and distinct.

B. A unique value of a exist for which the lines are coincident

C. Two values of a exist for which the lines are parallel

D. No value of a for which the lines are parallel.

We consider 3 non-aligne points in the plane. How many lines can one find that are exactly at the same distance from these three points?

Let x be an element of 0, [0, π]. We consider the inequalities {sinx>=[(2)^1/2]/2, 0<=cosx<(1/2). Which of the following statements is correct?

A. X is an element belonging to [π/4, π/3[;

B. X is an element belonging to ]π/4, 3π/4[

C. X is an element belonging to ]π/3, π]

D. X is an element beleonging to ]π/3, π/2]

Find the value(s) of x such that the angle between the vectors (0, 1, −1) and (−1, x, 0) is 2π/3 . Show all your calculations

Find the vector form of the equation of the plane passing through the point P (1-23) and has normal vector n <3,1, - 1>

find parametric equations of the line that passes through the point P =(2, 0,-1) and is parallel to the vector n =<2, 1, 3>

1.2 find paramedic equations of the line that passes through the points A= (1, 2, - 3) and B =(7, 2, - 4).

1.3 find paramedic equations for the line of intersection of the planes - 5x + y - 2z =3 and 2x - 3y + 5z =-7

Let L be the line given by (3,-1,2) + t (1,1,-1).Show that the above line L lies on the plane -2x + 3y -4z + 1 = 0

1.   Find the vector form of the equation of the plane that passes through the point P0 = (1, −2, 3) and has normal vector ~n =< 3, 1, −1 >.

2.   Find an equation for the plane that contains the line x = −1 + 3t, y = 5 + 3t, z = 2 + t and is parallel to the line of intersection of the planes x −2(y −1) + 3z = −1 and y = −2x −1 = 0.

3.   Find the point of intersection between the lines: < 3, −1, 2 > + t < 1, 1, −1 > and <−8, 2, 0 > + t < −3, 2, −7 >.

4.   Show that the lines x + 1 = 3t, y = 1, z + 5 = 2t for t ∈ R and x + 2 = s, y − 3 = −5s, z + 4 = −2s for t ∈ R intersect, and find the point of intersection.

5.   Find the point of intersection between the planes: −5x + y −2z = 3 and 2x −3y + 5z = −7.

1.1 find parametric equations of the line that passes through the point P =(2, 0,-1) and is parallel to the vector n =<2, 1, 3>

1.2 find paramedic equations of the line that passes through the points A= (1, 2, - 3) and B =(7, 2, - 4).

1.3 find paramedic equations for the line of intersection of the planes - 5x + y - 2z =3 and 2x - 3y + 5z =-7