092 Query

#$&*

course MTH 277

9/13 6:46

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 = <1,2,-3> + < -1,-2,3>

u + v = <0,0,0>

u - v = <1,2,-3> - < -1,-2,3>

u - v = <2,4,-6>

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

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

2u + 3v = 2 * <1,2,-3> + 3 * < -1,-2,3>

2u + 3v = <2,4,-6> + <-3,-6,9>

2u + 3v= <-1,-2,3>

confidence rating #$&*:

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

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

Given Solution:

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

Self-critique (if necessary):

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

Self-critique rating:

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

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 = 2^2

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

confidence rating #$&*:232;3

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

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

Given Solution:

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

Self-critique (if necessary):

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

Self-critique rating:

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

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

(x^2 - 2x +1 - 1) + (y^2 - 6y + 9 - 9) + (z^2 + 12z + 36 - 36) = 17

(x - 1)^2 + (y - 3)^2 + (z + 6)^2 = 17 + 1 + 9 + 36

(x - 1)^2 + (y - 3)^2 + (z + 6)^2 = 63

center (1, 3, -6)

radius= sqrt (63)

confidence rating #$&*:232;

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

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

Given Solution:

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

Self-critique (if necessary):

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

Self-critique rating:

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

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

PQ = [2 - (-3)]i + [-4 - 1]j + [-3 - 4]k

PQ = 5i - 5j - 7k

||PQ|| = sqrt (5^2 + (-5)^2 + (-7)^2)

||PQ|| = sqrt (25 + 25 + 49)

||PQ|| = sqrt (99)

||PQ|| ≈ 9.9499

confidence rating #$&*:232;

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

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

Given Solution:

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

Self-critique (if necessary):

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

Self-critique rating:

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

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

V = -i + (sqrt (3))j + 4k

||v|| = sqrt ((-1)^2 + (sqrt (3))^2 + 4^2)

||v|| = sqrt (1 + 3 + 16)

||v|| = sqrt (20)

u = (1/ (sqrt (20))) * (-i + (sqrt (3))j + 4k)

u = (-i/ sqrt (20)) + ((sqrt (3))j / sqrt (20)) + (4k / sqrt (20))

confidence rating #$&*:

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

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

Given Solution:

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

Self-critique (if necessary):

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

Self-critique rating:

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

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The graph of the cylindrical surface given by y = cos x is just the basic cosine curve with depth in the z-direction. When a cross section is taken parallel to the xy-axis, a parabolic shape is formed.

*** I am very unsure about my response to this question. I understand what the graph looks like but I don’t know how to “describe” it.

confidence rating #$&*:

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

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

Given Solution:

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

Self-critique (if necessary):

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

Self-critique rating:

@& It's like a curtain hanging in folds. When it reaches the floor the bottom seam of the curtain traces out a cosine graph. (actually the curtain continues on through the floor, its extent in all directions being infinite, but you get the picture)*@

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

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

v = i + (-3/2)j + 2k

u = sv ?

2i + 3j + (-4)k = s (i + (-3/2)j + 2k)

s = 2 2i + 3j + (-4)k = 2 (i + (-3/2)j + 2k)

2i + 3j + (-4)k = 2i - 3j + 4k

NOT PARALLEL

confidence rating #$&*:232;3

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

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

Given Solution:

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

Self-critique (if necessary):

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

Self-critique rating:

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

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:

||AB|| = sqrt [ (7-3)^2 + (1-0)^2 + (4-0)^2 ]

||AB|| = sqrt [ 4^2 + 1^2 + 4^2 ]

||AB|| = sqrt [ 16 + 1 + 16 ]

||AB|| = sqrt (33)

||BC|| = sqrt [ (5-7)^2 + (4-1)^2 + (4-4)^2 ]

||BC|| = sqrt [ (-2)^2 + 3^2 + 0^2 ]

||BC|| = sqrt [ 4 + 9 + 0 ]

||BC|| = sqrt (13)

||AC|| = sqrt [ (5-3)^2 + (4-0)^2 + (4-0)^2 ]

||AC|| = sqrt [ 2^2 + 4^2 + 4^2 ]

||AC|| = sqrt [ 4 + 16 + 16 ]

||AC|| = sqrt (36)

||AC|| = 6

[sqrt (33)]^2 + [sqrt (13)]^2 = 6^2

33 + 13 = 36

46 = 36

NEITHER

confidence rating #$&*:

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

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

Given Solution:

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

Self-critique (if necessary):

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

Self-critique rating:"

Self-critique (if necessary):

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

Self-critique rating:

Self-critique (if necessary):

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

Self-critique rating:

#*&!

@& You probably completed this before I posted the solutions. In any case you're in good shape here; you can check out and compare with my given solutions in the current version of the document. The explanations should be fine, and actually I expect the arithmetic is more accurate than on 9.3.*@

Self-critique (if necessary):

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

Self-critique rating:

#*&!

@& You probably completed this before I posted the solutions. In any case you're in good shape here; you can check out and compare with my given solutions in the current version of the document. The explanations should be fine, and actually I expect the arithmetic is more accurate than on 9.3.*@

#*&!