query 92

#$&*

course mth 277

9/14 11

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

.

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

At the end of this document, after the qa problems (which provide you with questions and solutions), there is a series of Questions, Problems and Exercises.

query_09_2

*********************************************

Question: Find u + v, u - v, (5/2)u, and 2u + 3v for the following vectors: u = <1,2,-3>, v = < -1,-2,3>.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

u + v=(1+-1,2+-2,-3+3)=(0,0,0)

u - v=(-1-1,-2-2,3- -3)= (-2,-4,6)

(5/2)u=(5/2)*<1,2,-3>=(5/2,5,-15/2)

2u + 3v =2*(1,2,-3)+3*(-1,-2,3)=(2,4,-6)+(-3,-6,9)=(-1,-2,3)

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):Okay

------------------------------------------------

Self-critique rating:3

*********************************************

Question: Find the standard form equation of the sphere with center (-1,2,4) and radius 2.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

(x+1)^2+(y-2)^2+(z-4)^2=4

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):okay

------------------------------------------------

Self-critique rating:3

*********************************************

Question: Find the center and radius of the sphere with equation x^2 + y^2 + z^2 - 2x - 6y + 12z - 17 = 0.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

x^2-2x+y^2-6y+z^2+12z=17

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

@& You need to complete the squares and compare with the standard notation for the equation of a sphere.

Checkl the current version of this document for a solution.*@

*********************************************

Question: Find the standard representation and length of PQ when P = (-3,1,4) and Q = (2,-4,-3).

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

5i-5j-7k

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):okay

------------------------------------------------

Self-critique rating:3

@& You also need to find the length, which I expect you know how to do. I believe you get sqrt(99).*@

*********************************************

Question: Find a unit vector in the direction of v = <-1, sqrt(3), 4>.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

( 1, sqrt(3), 4)/sqrt(1^2+ (sqrt(3))^2+ 4^2)= (1, sqrt(3), 4)/4.47= (.22i+.39j+.89k)

@& < > indicates a vector.

( ) would indicate a point.

The approximation is OK but yYou're better off using the exact value of the denominoator, which is sqrt(24), then doing the approximation at the end.*@

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):okay

------------------------------------------------

Self-critique rating:3

*********************************************

Question: Sketch and describe the cylindrical surface given by y = cos x.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The cos(x) has increases and deceases from 1 to -1 on the y axis.

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

Im a little unsure of what your asking .

------------------------------------------------

Self-critique rating:3

*********************************************

Question: Determine if u = 2i + 3j + -4k is parallel to v = <1,-3/2,2>.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

Take the unit vector of v= (1,-3/2,2)/sqrt(1^2+(-3/2)^2+2^2)=( 1,-3/2,2)/2.69=(.37i-.56j+.74k) u is not a multiple of the unit vector of v so it is not parallel

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):okay

------------------------------------------------

Self-critique rating:3

*********************************************

Question: Find the lengths of the sides of the triangle and determine if the triangle with vertices A(3,0,0), B(7,1,4) and C(5,4,4) is a right triangle, isosceles triangle, both, or neither.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

By my sketch I would say the triangle is a right triangle

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):okay

------------------------------------------------

Self-critique rating:3

@& A sketch never, ever proves anything about a triangle.

There are several ways to solve this.

You can find the vectors `AB, `AC and `BC, and see if the dot product of any of these vectors with any other is zero.

You could find the magnitudes of the three vectors and test the Pythagorean Theorem.

There are also other ways.*@

"

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

"

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

#*&!

@& I've inserted a few notes. Also be sure you check your solutions against those given in the current version of this document.*@