Analytic Geometry Answers

Which of the following statements is/are true? Explain why the false one is false. A. If u = (u1; u2) with ui not eqaual to 0 for some 1 <= i <= 2; then the unit vector in the direction of u is 1/sqrt( u1^2 +u2^2 )(u1; u2) : (2) B. u = (1; 2; 3) is the unit vector in the direction of u: (

Find the plane that passes through the point (2,5,3) and is perpendicular to the plane 2x-3y+4z+7=0

QUESTION 8

8.1 Let L1 and L2 be lines defined by

x = w0 + su, s ∈ R

and y = w1 + tv, t ∈ R, respectively.

Show that L1and L2 are parallel if and only if u = kv for some k ∈ R.
(8)

8.2 Find the plane that passes through the point (2, 4, −3) and is parallel to

the plane −2x + 4y − 5z + 6 = 0.
(4)

8.3 Find the line that passes through the point (2, 5, 3) and is perpendicular to the plane

2x − 3y + 4z + 7 = 0.
(4)

8.4 Find an equation of the plane passing through the point(−2, 3, 4) and is
perpendicular to the line passing through the points (4, −2, 5) and (0, 2, 4).
(4)

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What is the perimeter of △TUV?
Write your answer as an integer or as a decimal rounded to the nearest tenth.
Perimeter=
units
the coordinate points are T(-7,-9) V(3,10) U(6,-7)

A triangle has vertices A(-16,0) B(9,0) c(0,12).prove that the equation of the internal bisector of angle BAC of the triangle is x-3y+16=0

Let L1and L2 be the line defined by
x=wo+su and w1+tv
show that L1 and L2 are parallel if and only if u=if for some k €R

1) Let L1 and L2 be lines defined by :

x = w0 + su, s e R(element of R)
y= w1 + tv, t e R(element of R) respectively

Show that L1 and L2 are parallel if and only if u = kv for some k e R. (element of R)

2) Find the plane that passes through the point (2,4,-3) and is parallel to the plane - 2x + 4y - 5z + 6 = 0

3) Find the line that passes through the point (2,5,3) and is perpendicular to the plane 2x - 3y + 4z + 7 = 0

4) Find an equation of the plane passing through the point (-2,3,4) and is perpendicular to the line passing through the points (4,-2,5) and (0,2,4).

under what conditions are u + v and u − v orthogonal? Interpret your result geometrically

A triangle on a coordinate plane is translated to the rule T-3,-5(x,y). Which is another way to write this rule

Write an equation for the set of all points in the plane equidistant from (0, – 1) and y= – 5. Write your answer in vertex form. Simplify any fractions