9.8+OFSA+Solutions


 * OFSA SOLUTIONS for Vector Theory**

This page contains peer generated solutions and error explanations to OFSA questions. As you read or view the solutions, be critical: check for accuracy, but also for more efficient solution strategies. If you have a better method or different idea/answer, post a discussion and monitor the responses.


 * Quick Directions**
 * Post answers, solutions and error explanations to each OFSA question below.
 * For each "distractor" or incorrect answer choice, explain the error that would lead to that incorrect answer choice.
 * You may either do the above in typed format or using a pencast.
 * Separate each question with a section bar.
 * After each solution, provide a hyperlink back to the corresponding OFSA page.
 * Follow example below.
 * Click here to refer to solution format in 7.7

A - Might have thought it was the sum of all components B - Not the component of u onto v. It is the projection of u onto v. D - Might have been trying to find the projection of u onto v but accidentally did v onto u.
 * Question 1**
 * __Solution 1:__ C**
 * __Error Explanation 1:__**

Click here to return to OFSA.

A - Might have thought that the dot product meant to multiply the sum of the horizontal components by the sum of the vertical components C - Might have accidentally subtracted instead of added D - the answer is not a vector in component form, might have thought that it was vector in component form with the product of the horizontal components and the product of the vertical components as its horizontal and vertical components Click here to return to OFSA.
 * Question 2**
 * __Solution 2:__** B
 * __Error Explanation 2:__**

z=6i-7j converts to <6,-7> u+v-z=<2,5>+<3,7>+<6,-7> =<2+3-6,5+7+7>=<-1,19> which is -1+19j A- Arithmetic error B-Might of added all three vectors D-Might of thought different forms of writing vectors are incompatible. Click here to return to OFSA.
 * Question 3**
 * __Solution 3__**: C
 * __Error Explanation 3:__**

A-Might have mistakenly added B-The speed of the stream is not the speed of the swimmer as well C-Might have subtracted Click here to return to OFSA.
 * Question 4**
 * __Solution 4__**__: D__
 * __Error Explanation 4__**

For two vectors to be orthogonal, the dot product must be 0. Let us find the dot product of u and v: 243(5)-81k It must equal zero, so set the above expression equal to 0, and solve for k: 1215-81k=0, thus k= 15
 * Question 5**
 * __Solution 5:__** A

B-An error with sign change C-Might have added instead of multiplied to find the dot product D-Same as above Click here to return to OFSA.
 * __Error Explanation 5__**

A-An error with finding the magnitude of the first line (forgot to square the components-so they used root(4) instead of root(10) C-May have believed the y intercepts are added on to the y components of the vectors D-May have believed the y intercepts are added on to the y components of the vectors
 * Question 6**
 * __Solution 6:__** B
 * __Error Explanation 6__**

Link to a step by step solution to this problem: http://www.screenchomp.com/t/Lk4UkPsOP8BH

Click here to return to OFSA.

A-Did not recognize that the slope of the plane to create a circle must be 0 B-Did not recognize that the slope of the plane to create a hyperbola must be greater than 1 D-Did not recognize that the slope of the plane to create a parabola must be 1
 * Question 7**
 * __Solution 7:__** C
 * __Error Explanation 7__**

Image of Conic Sections and how they are formed: http://static.newworldencyclopedia.org/thumb/4/48/Conic_sections_2.png/450px-Conic_sections_2.png

Link to step by step solution to this problem: http://www.screenchomp.com/t/oM4xSvrgW

Click here to return to OFSA.

B-Found projection of v on u instead of u on v C-Forgot to multiply by v D-Found component of u onto v
 * Question 8**
 * __Solution 8:__** A
 * __Error Explanation 8__**

Link to step by step explanation to this problem: http://www.screenchomp.com/t/8ugOouMB0aY

Click here to return to OFSA.

math \cos^{-1}(u\bullet v/(|u||v|))= math math u\bullet v=3\ast -2 + 6\ast 5 math math math math math math \cos^{-1}(24/(3\sqrt{5}\ast \sqrt{29}))=48.37^{\circ} math A-Switched the negative sign from 2 to 5 and forgot to use cosine inverse to find angle. B-Used sine inverse. C-Forgot to use cosine inverse to find angle. Click here to return to OFSA.
 * Question 9**
 * __Solution 9:__** D
 * u|=\sqrt{3^2+6^2}
 * v|=\sqrt{(-2)^2+5^2}
 * __Error Explanation 9__**

math u_y=|u|\sin\theta math math u_y=25\sin(28^{\circ})=11.74 math B-Found the horizontal component instead by using |u|cos(28). C-Used square root of magnitude instead of actual magnitude. D-Used square root of magnitude and used cos(28) instead of sin(28). Click here to return to OFSA.
 * Question 10**
 * __Solution 10:__** A
 * __Error Explanation 10__**

math \hat{u}=u/|u| math math math math \hat{u}=<5,6>/\sqrt{61}=<5/\sqrt{61},6/\sqrt{61}> math A-Forgot to square root magnitude. B-Found magnitude only. D-Throw away. Multiplied two components together. Click here to return to OFSA.
 * Question 11**
 * __Solution 11__**:C
 * u|=\sqrt{5^2+6^2}
 * __Error Explanation 11__**

A - Found true speed B - thought it was the vector describing the true path D - wind vector Click here to return to OFSA.
 * Question 12**
 * __Solution 12:__** C
 * __Error Explanation -__**

A-Confused the tension of T2 as T1 C-Thought you had to multiply the weight (200 lbs) by 9.8 like in physics class and found the T1 for that D-Thought you had to multiply the weight (200 lbs) by 9.8 like in physics class and found the T2 for that
 * Question 13**
 * __Solution 13:__** B
 * __Error Explanation 13__**

Here's a step by step solution to this problem: http://www.screenchomp.com/t/bx7G1Fk3VS Click here to return to OFSA.

B-Multiplied the force, 50, by the distance between these two points C-Confused the vector for the slope as <2,1> instead of <1,2> D-Confused the 30 degrees for 20 degrees (because the problem on the examples and content pages were 20 degrees)
 * Question 14**
 * __Solution 14__**: A
 * __Error Explanation 14__**

Here's a step by step explanation to this problem: http://www.screenchomp.com/t/SdtHj6ie

Click here to return to OFSA.

Click here to return to OFSA.
 * Question 15**
 * __Solution 15__**
 * __Error Explanation 15__**

Click here to return to OFSA.
 * Question 16**
 * __Solution 16__**
 * __Error Explanation 16__**

Click here to return to OFSA.
 * Question 17**
 * __Solution 17__**
 * __Error Explanation 17__**

Click here to return to OFSA.
 * Question 18**
 * __Solution 18__**
 * __Error Explanation 18__**

Click here to return to OFSA.
 * Question 19**
 * __Solution 19__**
 * __Error Explanation 19__**

Click here to return to OFSA.
 * Question 20**
 * __Solution 20__**
 * __Error Explanation 20__**

Click here to return to OFSA.
 * Question 21**
 * __Solution 21__**
 * __Error Explanation 21__**

Click here to return to OFSA.
 * Question 22**
 * __Solution 22__**
 * __Error Explanation 22__**

Click here to return to OFSA.
 * Question 23**
 * __Solution 23__**
 * __Error Explanation 23__**

Click here to return to OFSA.
 * Question 24**
 * __Solution 24__**
 * __Error Explanation 24__**