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Find all vectors w = w 1 , w 2 , w 3 that satisfy the equation 1 , 1 , 1 × w = −1 , −1 , 2 .

w = w 3 1 , w 3 + 1 , w 3 , where w 3 is any real number

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Solve the equation w × 1 , 0 , −1 = 3 , 0 , 3 , where w = w 1 , w 2 , w 3 is a nonzero vector with a magnitude of 3 .

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[T] A mechanic uses a 12-in. wrench to turn a bolt. The wrench makes a 30 ° angle with the horizontal. If the mechanic applies a vertical force of 10 lb on the wrench handle, what is the magnitude of the torque at point P (see the following figure)? Express the answer in foot-pounds rounded to two decimal places.

This figure is the image of an open-end wrench. The lower portion of the wrench is at point P. The wrench has a length of “12 I n.” The angle the wrench makes with a horizontal line from P is 30 degrees. At the top of the wrench is a downward vertical vector labeled “10 l b.”

8.66 ft-lb

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[T] A boy applies the brakes on a bicycle by applying a downward force of 20 lb on the pedal when the 6-in. crank makes a 40 ° angle with the horizontal (see the following figure). Find the torque at point P . Express your answer in foot-pounds rounded to two decimal places.

This figure shows the pedals, cranks, and chain of a bicycle. The distance along the crank to the top pedal is 6 in. The angle of the crank is 40 degrees with the horizontal, measured toward the rear. The top pedal has a downward vector labeled “20 lb”.
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[T] Find the magnitude of the force that needs to be applied to the end of a 20-cm wrench located on the positive direction of the y -axis if the force is applied in the direction 0 , 1 , −2 and it produces a 100 N·m torque to the bolt located at the origin.

250 N

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[T] What is the magnitude of the force required to be applied to the end of a 1-ft wrench at an angle of 35 ° to produce a torque of 20 N·m?

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[T] The force vector F acting on a proton with an electric charge of 1.6 × 10 −19 C (in coulombs) moving in a magnetic field B where the velocity vector v is given by F = 1.6 × 10 −19 ( v × B ) (here, v is expressed in meters per second, B is in tesla [T], and F is in newtons [N]). Find the force that acts on a proton that moves in the xy -plane at velocity v = 10 5 i + 10 5 j (in meters per second) in a magnetic field given by B = 0.3 j .

F = 4.8 × 10 −15 k N

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[T] The force vector F acting on a proton with an electric charge of 1.6 × 10 −19 C moving in a magnetic field B where the velocity vector v is given by F = 1.6 × 10 −19 ( v × B ) (here, v is expressed in meters per second, B in T , and F in N ) . If the magnitude of force F acting on a proton is 5.9 × 10 −17 N and the proton is moving at the speed of 300 m/sec in magnetic field B of magnitude 2.4 T, find the angle between velocity vector v of the proton and magnetic field B . Express the answer in degrees rounded to the nearest integer.

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[T] Consider r ( t ) = cos t , sin t , 2 t the position vector of a particle at time t [ 0 , 30 ] , where the components of r are expressed in centimeters and time in seconds. Let O P be the position vector of the particle after 1 sec.

  1. Determine unit vector B ( t ) (called the binormal unit vector ) that has the direction of cross product vector v ( t ) × a ( t ) , where v ( t ) and a ( t ) are the instantaneous velocity vector and, respectively, the acceleration vector of the particle after t seconds.
  2. Use a CAS to visualize vectors v ( 1 ) , a ( 1 ) , and B ( 1 ) as vectors starting at point P along with the path of the particle.

a. B ( t ) = 2 sin t 5 , 2 cos t 5 , 1 5 ;
This figure is the first octant of the 3-dimensional coordinate system. There is a curve sketched that is increasing. On the curve is a point labeled “P.” At P there is a tangent vector to the curve labeled “v(1).” Also from P there is a vector towards the inside of the curve labeled “a(1).” Finally, there is a vector from P labeled “B(1)” pointing towards the z-axis.

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A solar panel is mounted on the roof of a house. The panel may be regarded as positioned at the points of coordinates (in meters) A ( 8 , 0 , 0 ) , B ( 8 , 18 , 0 ) , C ( 0 , 18 , 8 ) , and D ( 0 , 0 , 8 ) (see the following figure).

This figure shows a rectangular set of solar panels on a roof. The corners are labeled “A, B, C, D.” Also there is a vector drawn from A to D. There is another vector along the bottom of the rectangle from A to B.
  1. Find vector n = A B × A D perpendicular to the surface of the solar panels. Express the answer using standard unit vectors.
  2. Assume unit vector s = 1 3 i + 1 3 j + 1 3 k points toward the Sun at a particular time of the day and the flow of solar energy is F = 900 s (in watts per square meter [ W/m 2 ]). Find the predicted amount of electrical power the panel can produce, which is given by the dot product of vectors F and n (expressed in watts).
  3. Determine the angle of elevation of the Sun above the solar panel. Express the answer in degrees rounded to the nearest whole number. ( Hint : The angle between vectors n and s and the angle of elevation are complementary.)
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Questions & Answers

What is deflation
Aluko Reply
Enumerate emotional intelligence to a manager
Chinonso Reply
What about Sydney Alexander's Absorption approach in international trade?
Vibhas Reply
I need help in inflation graphs
Brandon Reply
Select inflation type, Demand pull, cost pull or anticipation 1- Select the set of data you intend on graphing i.e inflation rate of 2017, location (particular country) 2 - Select the type of measurement tool that best allows you to input the inflation data, Consumer price index is the most accurate
this is to make sure you have all the correct information, Also use should know 1- Cost pull is Aggregate Demand and Aggregate Supply AD - AS graphed 2- Demans pull is Aggregate Supply and Aggregate Demand AS - AD graphed
what is production
Imoro Reply
what is a monopolistic competition?
moniman Reply
Enumerate emotional intelligence to a manager
Enumerate emotional intelligence to a manager
who is barter
Tening Reply
exchange goods each other
what is economic
is the use of scares resources to satisfy our unlimited needs and wants
how many kinds of utility functions?
What is partnership?
the legal association of two or more people as co-owners of a business for profit.
Would you expect the kinked demand curve to be more extreme (like a right angle) or less extreme (like a normal demand curve) if each firm in the cartel produces a near-identical product like OPEC and petroleum? What if each firm produces a somewhat different product?
James Reply
what is supply
Mizta Reply
what is opportunity cost
The opportunity gained interms of opportunity lost is known as opportunity cost Or The second best alternative use of resources
forgone alternative: like forgoing Something our of two to buy one
what is macro economic s
Addo Reply
macroeconomics is the study of economic as a whole level.
meaning of positive science
Sumit Reply
positive science it is focused on facts and cause and effect and behavioural relationship and include developmental testing in economic theoreis.
what is inflation
Sama Reply
inflation is the general price increase of goods and services in an economy.
Inflation is the persistent rise in the general price level
inflation is characterized by increase in the general price of goods and services. when there is too much money in circulation. increase in demand of goods pursuing fewer goods. when purchasing power of money decreases .
inflation is the persistent rise general price level
inflation is the persistent increase in price
how are you
increase in the general level of price...
what is deflation
is the gradual decrease of currency exchange in a country.
why ecnomics important ? give answer plz
Because is a field of science study that reflects on our day to day activities with human behavior.
why economic is a science
Economics is referred to as a social science not a pure science. It's regarded as a social science because it makes use of the scientific method to solve problems. The scientific method refers to observation, asking questions, forming hypothesis, experimentation etc
Economics is a social science because it study human behavior how he relates with his daily activities with the available limited resources to satisfy his wants.
what are the factors affecting the demand
yeah it uses the scientific method to study human behaviour.
inflation referes to the persistant increase in the general price of goods and services over a given period of time say a year.
factors affacting Demand of good and services are 1.price of a commodity in question 2.price of related commodity 3.Income of a consumer 4.Population 5.tast and prefereance 6.Season or weather condition
what is difference between perfect and non perfect market.
what the difference between Trade off and Opportunity Cost?
In trade off, you increase the amount of something by decreasing the amount of something else. For example, you use 2 hours to study and 2 hours for leisure. if you increase study hour by 1 more hour, i.e 3 hours, leisure time will decrease by 1 hour, i.e 1 hour.
In all, you would have traded off 1 hour of leisure time for 3 hours of study time. But in opportunity cost, you let something go in order to obtain something else entirely.
thanks for your idea
please i want help on thid question given P=$10 And TC=120+4Q2 1.find the profit maximizing level of price and quantity. 2.what will be the total profit?
please how is substitutional effect affecting demand
if a price of a particular commodity is high people demand less ,they rather go for less one
what is account
account is an arrangement between a customer and a bank that allows the customer to play in and take out money (bank account)
pay, not play sorry
four effects of inflation in an economy
decreases living standards .. decreases purchasing power.. Decreases internation competition . increases the cost of borrowing
Inflation refers to persistent increase in the general prices of commodities.
he asked for effects
Low standard of living, prices of commodities will be high, devaluation of currency in the economy
Debtors gain while creditors loses
Hi every one
how are you all
Fin and you
me also
Whare do you live
general tendency of rising price and continuous... .
any one among you is going to aaper in net exam day after tomorrow
Oo Pakistan I am India
really from Pakistan
You noo hindi
what is deference between the producer and firm?
different between demand and quantity demand
Farhan Reply
No difference
demand is the overall demand for it
actually theres no difference
quantity demanded is used in Equilibrium of d and s
for evrything else u use deman
the difference of it is that when demand simply denotes the willingness and a person's ability to purchase. And as against quantity demand represent the amount of an economic good or services desire by a consumer at a fixed price .☺
how to calculate inflation
Richard Reply
Explain the factors that have led to high quantity demanded
Ogwang Reply
price of the product increase of price substitute product as people shift to cheap one
in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
Leah Reply
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Practice Key Terms 6

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Source:  OpenStax, Calculus volume 3. OpenStax CNX. Feb 05, 2016 Download for free at http://legacy.cnx.org/content/col11966/1.2
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