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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 ;
b.
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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
can you provide the details of the parametric equations for the lines that defince doubly-ruled surfeces (huperbolids of one sheet and hyperbolic paraboloid). Can you explain each of the variables in the equations?
Radek Reply
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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