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 Distance Formula:

Equation of a 3D Sphere:

Calculus 3 - Intro to Vectors:

Calculus 3 - The Dot Product:

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Angle Between Two Vectors:

Parallel & Orthogonal Vectors:

Direction Cosines and Vectors:

Calculus 3 - Vector Projections:

Cross Product of 2 Vectors:

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Area - Vector Cross Product:

Triple Scalar Product:

Vector Equations of Lines:

The Equation of a Plane:

Planar Equation - 3 Points:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

Vectors - Free Formula Sheet:

[truefupu]

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[ebhojayejuliet]

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[gamerking]

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[georgesadler]

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 YouTube TV with the Organic Chemistry Tutor.

[Benedict_Miriti]

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[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

[sjpbrooklyn]

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)).

[Alfurwan]

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[sovikdey]

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[starstruck]

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

[lamarts]

Crystal clear explanation! Awesome job!!! Thanks

[TheJHNSN]

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[joebryansamson]

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

[lanomusambazi]

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

[PunmasterSTP]

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

[alphaomarjallow]

Thank you so much sir, really appreciated.

[icecreamlover]

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.

[isabelleortiz]

I love you. My professor talks so slow omg.

[hktears]

Can you do next motion in physics please

[kelvinmaina]

thanks....you really explain perfectly