Analytic Geometry Answers

The equation x2−8 x+y2− 14 y+z2+ 16 z= -113 represents a sphere with radius Blank 1. Calculate the answer by read surrounding text.

and center ( Blank 2. Calculate the answer by read surrounding text.

, Blank 3. Calculate the answer by read surrounding text.

, Blank 4. Calculate the answer by read surrounding text.

).

Question 3 of 12 3 Points

Fit the equation with the surface in R3

A. Plane parallel to the xz-plane.

B. Plane parallel to the yz-plane.

C. A circle with radius 2.

D. Circular cylinder with radius 2.

E. Sphere with radius 2 and center (3,5,−1)

F. Sphere with radius 2 and center (−3,−5,−1)

select

1. x2+y2=4

select

2. x2+y2=4,z=4

select

3. 6x+x2−10y+y2+2z+z2=−31

select

4. 6x+x2+10y+y2+2z+z2=−31

select

5. x=3

select

6. y=3

Two nonzero vectors a and b are called perpendicular or orthogonal if the angle between them is Blank 1. Fill in the blank, read surrounding text.

and a⋅ b= Blank 2. Fill in the blank, read surrounding text.

.

If a and b denote the vectors OA and OB, indicate on the same diagram the vectors OC and OD denoted by a +b and a-b. Draw on another diagram the vector OE denoted by a + 2b.

find the value(s) of t so that the distance from P(3,4) to R(t,8) is 4√2

If the position vector of A and B are 3

−→a − 7

−→b − 7

−→c and 5

−→a + 4

−→b + 3−→c , nd −→AB

and determine its magnitude and direction cosines.

Determine whether any of the lines are parallel or identical.

L1: x = 3 + 2t, y = −6t, z = 1 − 2t,

L2: x = 1 + 2t, y = −1 − t, z = 3t,

L3: x = −1 + 2t, y = 3 − 10t, z = 1 − 4t,

L4: x = 5 + 2t, y = 1 − t, z = 8 + 3t.

3a. Consider the line L that passes through the point P₀(4, 2, -3) is parallel to the vector

⟶ [ 2

u = -1 <----Matrix

6]

Find a vector equation and the parametric equations of the line L.

b. Find the point of intersection of the line L with the xy-plane (z = 0).