Analytic Geometry Answers

Find the equation of the right circular cone whose vertex is (2, 1, 0), semivertical angle is 30° and the axis is the line x-2/3=y-1/1=z/2

(3.1) Find an expression for 12 || ~ u + ~ v || 2 + 12 || ~ u − ~ v || 2 in terms of || ~ u || 2 + || ~ v || 2

(3.2) Find an expression for || ~ u + ~ v || 2 − || ~ u − ~ v || 2 in terms of ~ u · ~ v

3.3) Use the result of (3.2) to deduce an expression for || ~ u + ~ v || 2 whenever ~ u and ~ v are orthogonal

to each other.

In a cartesian plane xy.The line which passes through the origin and is perpendicular to the line of equation 5x-3y-1=0 has for equation?

A. 3x-5x=0

B. 3x+5y=0

C. 5x-3y=0

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