query 91

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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_1

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Question: Sketch the vector from P to Q, write it into standard component form, and find ||PQ||. P=(4,-1) Q=(-3,7).

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Your solution:

-7i+8j

||PQ||= sqrt((-7)^2+(8)^2)=sqrt(113)=10.63

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):okay

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Self-critique rating:3

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Question: Let u = <-4,3> and v = <2,-1/2>. Find scalars s and t so that s * <0,3> + tu = v.

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Your solution:

S*<0,3>+t<-4,3>=<2,-1/2>

S=2/3 and t=-1/2

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):okay

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Self-critique rating:3

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Question: Let u = 4i - 3j, v = -3i + 4j , and w = 6i - 3j. Write the expression ||u|| ||v|| w in standard form.

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Your solution:

||u||=sqrt(4^2+(-3)^2)=5

||v|| =sqrt((-3)^2+4^2)=5

Plug into expression ||u|| ||v|| w =5*5* (6i-3j)= 150i-75j

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):okay

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Self-critique rating:3

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Question: Let u = 4i + j, v = 4i + 3j, w = -i + 2j. Find a vector of length 3 with the same direction as u - 2v + 2w.

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Your solution:

(4i+j)-2(4i+3j)+2(-i+2j)=(4-8-2)i+(1-6+4)j= -6i-1j

(-6i-1j)/sqrt((-6)^2+(-1)^2)= (-6i-1j)/6.08= -.99i-.16j is the unit vector

Then you multiply the unit vector by 3 = 3*(-.99i-.16j)= -2.97i-48j

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):okay

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Self-critique rating:3

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Question: Show that the vector v = cos(theta)i + sin(theta)j is a unit vector for any angle theta.

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Your solution:

cos(theta)i + sin(theta)j/sqrt((cos(theta))^2i + (sin(theta))^2j)

= cos(theta)i + sin(theta)j/sqrt(1)= cos(theta)i + sin(theta)j/1= cos(theta)i + sin(theta)j

The unit vector is cos(theta)i + sin(theta)j because of a identity.

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):okay

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Self-critique rating:3

@& All you really need to say is that the magnitude of the vector is sqrt((cos(theta))^2 + (sin(theta))^2 ), which is equal to 1.

i and j are not part of the expression for the magnitude of this vector.*@

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Self-critique (if necessary):

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Self-critique rating:

"

Self-critique (if necessary):

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Self-critique rating:

#*&!

@& Good work, but be sure to check my note for a couple of details.*@