9.6+OFSA

OFSA for Vector Theory
This page contains peer generated questions that help you assess your understanding. Remember that questions may not represent the rigor of the questions you may be expected to complete on formal assessments. This page is simply an OFSA - opportunity for self assessment.

math {\text{Given: }u=<3,7> \text{ and } v=<4,5> {\text{What is the component of u onto v?}
 * Question 1**

\begin{array}{*{20}{l}} &{19}}&{} \\ &{ <\frac{188}{\sqrt{41}},\frac{235}{\sqrt{41}}> }&{} \\ &{7.34}&{} \\ &{ <\frac{141}{\sqrt{58}},\frac{329}{\sqrt{58}}> }&{} \end{array} math

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math {\text{Given: } u=<1,3> \text{ and } v=<5,2> {\text{Evaluate: } u\cdot v
 * Question 2**

\begin{array}{*{20}{l}} &{30}}&{} \\ &{ 11 }&{} \\ &{-1}&{} \\ &{ <5,6> }&{} \end{array} math

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math {\text{Given: } u=<2,5> \text{ and } v=<3,7> \text { and } z=6i-7j \text{, find u+v-z.}
 * Question 3**

\begin{array}{*{20}{l}} &{<-1,5>}&{} \\ &{ 11i+5j }&{} \\ &{-i+19j}&{} \\ &{ \text{Not possible}}&{} \end{array} math

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math {\text{A swimmer is attempting to cross a stream. Normally, he swims at 15 mph without a current. However, today there is a current going 20 mph downstream, what is the swimmer's actual speed}?
 * Question 4**

\begin{array}{*{20}{l}} &{\text{35 mph}}&{} \\ &{ \text{20 mph}}&{} \\ &{\text{5 mph}}&{} \\ &{\text{25 mph}}&{} \end{array} math

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math {\text{If, } u=<243,-81> \text{ and } v=<5,k> \text{, for what value of k would the two vectors be orthogonal?}
 * Question 5**

\begin{array}{*{20}{l}} &{15}&{} \\ &{-15}&{} \\ &{-167}&{} \\ &{167}&{} \end{array} math

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If line a is defined as y=3x+4 and line b is defined as y=-5/7x+14, what is the angle measure in degrees that is formed between these two lines? math \begin{array}{*{20}{l}} &{62.29}&{} \\ &{72.90}&{} \\ &{28.35}&{} \\ &{4.5}&{} \end{array} math
 * Question 6**

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math {\text{If } u=<291,-22> \text{, what conic section would be formed if this vector represented a plane used to cut a cone?}
 * Question 7**

\begin{array}{*{20}{l}} &{\text{circle}}&{} \\ &{\text{hyperbola}}&{} \\ &{\text{ellipse}}&{} \\ &{\text{parabola}}&{} \end{array} math

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math {\text{Find the projection of u on v if } u=<3,4> \text{ and } v=<-4,7>.
 * Question 8**

\begin{array}{*{20}{l}} &{<-64/65, 112/65>}&{} \\ &{ <48/25, 64/25? }&{} \\ &{16/65}&{} \\ &{ 16/\sqrt{65}}&{} \end{array} math

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math {\text{Find the angle between vectors } u=<3,6> \text{and } v=<-2,5>.
 * Question 9**

\begin{array}{*{20}{l}} &{-8\sqrt{145}/145}&{} \\ &{ 41.63^{\circ} }&{} \\ &{8\sqrt{145}/145}&{} \\ &{48.37^{\circ}}&{} \end{array} math

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math {\text{Find the vertical component of } |u|=25 \text{ and the angle of the vector is } 28^{\circ}.
 * Question 10**

\begin{array}{*{20}{l}} &{11.74}&{} \\ &{22.07}&{} \\ &{2.35}&{} \\ &{4.41}&{} \end{array} math

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math {\text{If } u=<5,6> \text{, what is the unit vector(} \hat{u} \text{)?}
 * Question 11**

\begin{array}{*{20}{l}} &{<5/61, 6/61>}&{} \\ &{ 61 }&{} \\ &{<5/\sqrt{61}, 6/\sqrt{61}>}&{} \\ &{30}&{} \end{array} math

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math {\text{An airplane is flying directly Northeast at 50 mph. There is a crosswind blowing 80 mph S } 30^{\circ} \text{ W. What is the true direction of the plane?}
 * Question 12**

\begin{array}{*{20}{l}} &{104.74 \text{mph}}&{} \\ &{ <104.637, -4.645> }&{} \\ &{357.456^{\circ}}&{} \\ &{<80cos330^{\circ}, 80sin330^{\circ}}&{} \end{array} math

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Two strings, T1 and T2, are holding up a 200 pound object. T1 makes a 35 degree angle with the horizontal and travels in the northwest direction. T2 makes a 25 degree angle with the horizontal and is in the northeast direction. Find the tension on T1. A. 189.18 B. 209.30 C. 2051.16 D. 1853.91 Click here for solution.
 * Question 13**

How much work would it take if you were pulling a box with 50 N of force at an angle of 30 degrees from the point (3,1) to (4,4)? A. 93.30 B. 111.80 C.111.60 D.81.19 Click here for solution.
 * Question 14**

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 * Question 15**

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 * Question 16**

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 * Question 17**

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 * Question 18**

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 * Question 19**

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 * Question 20**

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 * Question 22**

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 * Question 23**

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 * Question 24**