Calculus 3 - Direction Cosines & Direction Angles of a Vector

This calculus 3 video tutorial explains how to find the direction cosines of a vector as well as the direction angles of a vector.
3D Coordinate System: • Plotting Points In a T...
3D Distance Formula:
• How To Find The Distan...
Equation of a 3D Sphere:
• How To Find The Equati...
Calculus 3 - Intro to Vectors:
• Calculus 3 - Intro To ...
Calculus 3 - The Dot Product:
• Calculus 3 - The Dot P...
_______________________________
Angle Between Two Vectors:
• Finding The Angle Betw...
Parallel & Orthogonal Vectors:
• Are The Two Vectors Pa...
Direction Cosines and Vectors:
• Calculus 3 - Direction...
Calculus 3 - Vector Projections:
• Calculus 3 - Vector Pr...
Cross Product of 2 Vectors:
• Cross Product of Two V...
_______________________________
Area - Vector Cross Product:
• Area of a Parallelogra...
Triple Scalar Product:
• Volume of a Parallelep...
Vector Equations of Lines:
• How To Find The Vector...
The Equation of a Plane:
• How To Find The Equati...
Planar Equation - 3 Points:
• How To Find The Equati...
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Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Vectors - Free Formula Sheet:
bit.ly/3WYIGOv

[@TheOrganicChemistryTutor]

Vectors - Free Formula Sheet: bit.ly/3WYIGOv
Final Exams and Video Playlists: www.video-tutor.net/

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from 2018 to now literally every calculus chemistry and physics student has passed their classes thanks to him

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Also Mathematics and Physical Sciences teachers

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[@PunmasterSTP]

Wow that's awesome! How have your classes at Stanford been going?

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[@PunmasterSTP]

@@lindajia3181I don't take a lot of things at face value, but was still curious and figured I'd reply. I've made a habit of replying to a lot of comments, because a fraction of the time it does lead to a cool conversation.

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for a solid explanation of Direction Cosines and Direction Angles of a Vector in Calculus Three. Direction Cosines and Direction Angles of a Vector are also used in Engineering Statics and Dynamics. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.

[@gamerking6668]

Ya'll know what?
This guy teaches better than my physics teacher.
As my experience, when I searched up this topic on RUclips, Other RUclips channels showed crap. But this guy really saved my day.... I highly recommend this channel

[@PunmasterSTP]

How'd the rest of your physics class go?

[@Benedict_Miriti]

Thank you so much.You're literally a great math tutor.

[@itsurenkanakueta]

I get it fully, I think because they say u feel like you understand every time when listening but forget it but the fact that I feel the feeling of being able to understand makes you a great teacher

[@Alfurwan]

your videos are a breath of fresh air in my feed!

[@sjpbrooklyn7699]

Thank you for a well-done systematic and logical explanation. Some of your viewers might be surprised to find a geometry lecture under the heading of organic chemistry, but it would definitely have helped me many years ago when I was doing my doctoral dissertation in polymer chemistry at NYU. I “built” computer models of polyethylene for Monte Carlo simulations of polyethylene conformation by placing the first carbon at the origin (I ignored hydrogens) and calculating the coordinates of each successive atom along the chain using a tetrahedral bond angle (arccos (-1/3)) and bond length of 1.54 Å. So far the vector algebra is fairly simple. It steps up a notch when you have to specify the torsional (dihedral) angle for four consecutive atoms (i.e., the angle between the plane of atoms 1, 2, & 3 and the plane of atoms 2, 3, & 4. Each Monte Carlo step consisted of choosing one of the polyethylene bonds at random and then rotating all of the atoms after that bond through a random angle phi between 0 and 360 deg., about the projection of that bond, leading to a new conformation which differed from the preceding one by exactly one dihedral angle. I then calculated the energy of the new conformation and used the Metropolis sampling method (adapted by Unilever chemist Moti Lal) to either accept the new conformation or keep the old one. A Monte Carlo “experiment” consisted of doing this thousands of times, so that the “molecule” executed a Markoffian random walk in “conformation space” defined by the vector of torsional angles. It was the rotational geometry that my notebook says took me about a month to figure out with the help of Margenau and Murphy’s classic textbook The Mathematics of Physics and Chemistry. (Murphy, who co-discovered deuterium with Urey, was my course instructor. Urey won a Nobel prize but Murphy did not). For a given atom beyond the rotation point the new coordinate vector is N = QA where A is the old coordinate vector. Q = D-inverse x R x D where D is the matrix of direction cosines relating the new coordinate system for that atom to its original system, and R is a 3x3 matrix whose rows are (1,0,0), (0, cos(phi), sin(phi)), and (0, -sin(phi), cos(phi)).

[@starstruck7086]

my man what a legend can you make a vid that is focusing on 3d vectors, like bro ur the reason im still surviving engineering

[@radirandom]

me too. ENG

[@sovikdey4287]

organic chemist teaching maths....thats great

[@devotionalstories3731]

Yes an expert of organic chemistry can teach Mathematics very nicely.
Many concepts in chemistry have their foundation in Mathematics.
Every compound has a structure and configuration with molecular bonding
Also the hydrocarbons are named according to C in functional ground like butane for 4 C and hexane for 5C.

[@lamarts1000]

Crystal clear explanation! Awesome job!!! Thanks

[@sribakiyav5455]

The way of teaching is just awesome 👌

[@leepatrick1756]

Thanks! Perfectly clear at last!

[@TheJHNSN]

You’ve saved my academic life. You’re the best!

[@lanomusambazi8654]

Thank you sir for the video. I have now understood the concept of direction cosines and and angles.

[@icecreamlover7072]

Shouldn't arc cos cancel the negative sign? As it is an even function. When I put 6/√61 I get 39.8° and when I put -6/√61 I get 140.2° while both should be same right? Please clear this to me.

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just the best tutor in the world, thank your sir!!

[@PunmasterSTP]

Direction cosines? More like "Dang good information that informs and saves!" 👍

[@alphaomarjallow1751]

Thank you so much sir , really appreciated.

[@hktears3167]

Can you do next motion in physics please

[@kelvinmaina1189]

thanks....you really explain perfectly

[@prodyungbvx7800]

You are better then my Calculus teacher. Btw, i study this in calculus 1(?!), is that normal lol

[@isabelleortiz6895]

I love you. My professor talks so slow omg.

[@canozturk369]

thank you from Turkey

[@MuhammadAkmal-fm1tl]

Why we take only 'cos' ???

[@tilteddingo4679]

Smart people figured it out I would guess

[@mdzaidhassan8996]

Basic trignometry...
Cos is base upon hypotenuse

[@rajdeepnaha1242]

To take the vector along x y z

[@saki7952]

I'm one of the first 100 to see your video.

[@rawstone4579]

Geogebra tells me that the angle is 68 between x axis and and vector, while your video states the angle is 72.65. What is wrong?

[@klasta2167]

you

[@faithnelo8545]

Thank you

[@siabi971]

2:27 end of a very useful info

[@architahait8466]

Video was extremely helfpul

[@Lanaka-jd3hf]

Just a quick question can I be asked to find v onto u

[@zhandoshumyrbek9814]

Who knows? Why sum of squares of the direction cosines must be equal to ?

[@Chevron_]

If you square and sum all the numerators, you will get (v_x)^2+(v_y)^2+(v_z)^2.
Since the denominators are the same when we add the fractions, the final denominator will be the magnitude of the vector squared.
The magnitude of the vector is given by sqrrt( (v_x)^2+(v_y)^2+(v_z)^2) ), so when we square it we get (v_x)^2+(v_y)^2+(v_z)^2.
(v_x)^2+(v_y)^2+(v_z)^2 / (v_x)^2+(v_y)^2+(v_z)^2 = 1 because they are the same
My apologies for the poorly presented maths, the equations look clunky because I can't write the operations in a youtube comment

[@kunalthapar4603]

But why cosine?? Any idea??

[@yousefahmed1336]

You're the best.

[@user-oy5wk9wp6e]

can't believe my school is making me do this in precalculus

[@mkamalakkannan8327]

My mathematics teacher keep us always in jungles or deserts.

[@ridwanahmed9330]

Thank you buddy.

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I think its safe to call you the Richard Feynman of our generation

[@malakasadalikhan109]

2:15 3:03 3:10
4:30Example

[@miloslavpetras713]

Very nice

[@saanvisharma2126]

How do you calculate the value of the arccosine?

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God bless you

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U are awsome

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thanks

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AMAZING

[@n9583]

Thank

[@Regolith]

is a vector basically just a 3D angle

[@lifecraft3679]

2:26

[@matthewerwine8333]

I thought gamma was written as Y

[@nightshade1807]

2:25

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Maths was hated by most of the people the crush of some people but

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to watch

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Man I need help anyone please I have vectors in my exam after tmr and the book is useless as shit and all the vector videos don't match my questions 😭😭😭😭

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Without explaining the principle of how to get the direction cosines, dude all what I can say is, shit.

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