Are The Two Vectors Parallel, Orthogonal, or Neither?

This calculus 3 video tutorial explains how to determine if two vectors are parallel, orthogonal, or neither using the dot product and slope.

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 Formula Sheet:

[malakasadalikhan]

Quick test: Calculate Slope (when slopes of both vectors are negative reciprocals of each other) 2:20
Orthogonal when dot product is zero meaning the two vectors are perpendicular to each other 2:38
Another Method Calculate Angle 7:59

Parallel: 4:20

8:50 Summary

[richardblkmann]

the rain in the background made this very relaxing

[crneymar]

this dude literally knows everything about math

[tippyandfriend]

I like how you used the simple graphs to explain the concept. Very approachable way into understanding the concept. Thank you for this.

[aeza]

Thank you so much! Your videos are so easy understand and SO helpful!

[ivashehu]

So much more helpful than any other explanation out there! Thank you!

[curlyfries]

Im convinced you are the smartest mind according to youtube history

[georgesadler]

Professor Organic Chemistry Tutor, thank you for another great video/lecture in Calculus, which shows if two vectors are Parallel, Orthogonal or Neither. These are powerful tools in all levels of Pure/Applied Mathematics. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

[j.t]

All of your videos are really helpful.

[kylilmorrow]

when will there be more calc 3 videos? my class has just started the Dot product

[angelalv]

3:28 you said they are orthogonal but isn’t orthogonal when they are 90degrees . So since it’s 0 aren’t are parallel???

[The_Marcelo]

Can you do more linear algebra videos pls

[dansh]

thank you man, that was very helpful.

[dusanmitrovic]

keep on going baby ur an angel bless u

[SteveBillyy]

Does this apply to vectors with a z axel? When checking the magnitude of (8, 4, 12) do you ignore the z axis?

[yhsvbcv]

But similar slopes and angles do not guarantee perpendicularity, what if the two vectors are collinear?

[maheletmahelet]

thank u too much but do u have a video to test collinear vector

[MIchaelArlowe]

Is 270 degrees also considered orthogonal?