Math21a. Vector Projection Equations

A discussion of the vector projection and the scalar component equations.

[@prometheus05dev56]

The only video I found where it is not said "I'm gonna drop this formula her" but shown mathematically why it is this way, thanks alot!

[@KatePenner]

Truly my teaching pet peeve! Like these things just appear out of thin air or something... they don't!

[@xNinjaTovarx]

Very, very clear and concise. Thank you for publicly sharing!

[@KatePenner]

You're welcome!

[@oceanview3165]

This the video I have been looking for. you are awesome ! Pls make more videos like this for multivariable calculus .

[@windthorpe9628]

Thank you so much! I have been searching online for a few days to find out the distinction between the component and projection vectors, and you explained it so well!

[@KatePenner]

Thank you! Glad you found it helpful!

[@VivekSingh-nt2zv]

kzbin.info/www/bejne/ZofQi2ivgJ6Hhrs&ab_channel=Sunyamekam

[@parthrawri3001]

Awesome! I love you! :3

[@pheonixeye_1162]

You're an angel Saved my day.

[@theadel8591]

Thanks, you’re a good person 💐

[@fowzh4659]

THANK YOU SOSOSO MUCH VEDRY GREAT VIDEO

[@ConceptualCalculus]

The best vid on this topic that I have found. Thank you.

[@KatePenner]

I really appreciate it! I'm glad you found it helpful.

[@amitmodak21]

Excellent. Made me get a good intuitive understanding of this concept.

[@KatePenner]

Awesome! That is what I like to hear!

[@ndebelesammie]

That's awesome, so clear. Thank you

[@KatePenner]

You're welcome!

[@listowel33shepherd9]

Thank you so much Exactly what I was looking for

[@internationalremixes6440]

thanku mam....that was tooo nice

[@sangrambiswal7378]

Nice video it clear all doubt of mine. I like u & yr simple explanation.....

[@KatePenner]

Thank you so much!

[@guyreefer7086]

Best explanation ever!!! God bless you sweet lady... please do share your intuitive knowledge with those of us who thirst. I will subscribe right now

[@KatePenner]

You're welcome! Definitely working on some additional content on the break between semesters!

[@tv58349]

👍

[@ashwaniyadav3661]

Thank you so much, Ma'am. I was having hard time figuring it out. Love from India

[@KatePenner]

So glad you found the video helpful!

[@VivekSingh-nt2zv]

kzbin.info/www/bejne/ZofQi2ivgJ6Hhrs&ab_channel=Sunyamekam

[@TruongNg9x]

Such a great video. My teacher made everything so complicated and unclear

[@KatePenner]

I'm sorry to hear that you had a hard time in class, but I'm so glad I could help!

[@johnwdsouza1]

Very useful

[@HassanAli-sy5rk]

Very nice. Keep it up

[@kristinmai8636]

Thanks a lot!! I finally understand this!

[@KatePenner]

YES that is what we like to hear!

[@vincentjoyhere]

At last I understood this. Thanks very much.

[@KatePenner]

Fantastic! Glad I could be of help!

[@enes5345]

thank you

[@KatePenner]

You're welcome!

[@lux27.42]

Thank you, so much

[@KatePenner]

You're welcome! Happy to help!

[@srivijayamadhuri839]

Thanking u respected madams and sirs for giving excellent explinations

[@KatePenner]

You're very welcome! Thanks for watching!

[@acsu96]

Thanks Kate!

[@KatePenner]

You're welcome!!

[@aabhasdhaubanja1184]

Very very nice 💗💗💗💗

[@arunbm123]

brilliant lecture....nice

[@KatePenner]

Thank you - glad you found it helpful! -KP

[@kosisochukwuezewudo4688]

Thanks so much!!

[@KatePenner]

Of course!

[@oscarobioha595]

this has been really helpfull, it would be great if u also did the same for distributivity and commutativity. Thank u

[@KatePenner]

I will put this on the list of videos I am making! Thank you for the suggestion!

[@HassanAli-sy5rk]

❤❤💙💙💜💜💚💚

[@rohanthomas5434]

Thanks a lot 🙂

[@KatePenner]

You're welcome 😊!!

[@JatinSaini543]

Hi,thanks for this wonderful explanation.I just have one doubt.As you explained that projection of a onto b is =(component of b )* (direction of a).And in the first line you mentioned component of b= |b| cos@.so can we write projection of b onto a =(|b| cos@)(a/|a|).

[@KatePenner]

Yes, that's a valid rewriting! However, since we are more often given the two vectors, and not the angle between them, the form with the dot product is usually more useful (since we frequently won't know theta).

[@YAHSHUA777]

Because I'm committing crimes with BOTH DIRECTION AND MAGNITUDE, OH YEAAAAAH!!!!!!

[@KatePenner]

This gave me a good chuckle! Hope you found the vid helpful.

[@Alia-rw9ti]

thankyou

[@KatePenner]

You're welcome!

[@theadel8591]

So the component is the magnitude of the new vector that’s parallel to one of the original vectors and a component of the other ?

[@KatePenner]

yes - that's a great way of putting it!

[@KatePenner]

Ignore this if it confuses you, but building on what you said... you could take a particular vector and make it the hypotenuse of an infinite number of right triangles. (Draw a few if you don't believe me!) Once you get specific and select another vector to be the *direction* of the base (note that the base itself could be longer or shorter, or pointed in the opposite direction, but parallel to this vector), you now have only one right triangle that is possible to construct! The vector projection is that vector -- it is the base of a right triangle (with your first vector as the hypotenuse) parallel to the other vector. The scalar projection is the length of the base. It will be a negative number if the base of the right triangle and the vector you are projecting onto are pointing in opposite directions!

[@BindhuJBSG]

Is it necessary that both the vectors starts from the same point

[@KatePenner]

Hi Bindhu! Vectors *in general* do not have specific anchor points, but when we write something like that could start *anywhere in space*, increase one unit in the x-direction, and end. However, when discussing scalar components, it is necessary to visualize the two vectors you are working with to be anchored at the same point to make sense of the measurement you are calculating. This won't change anything about how those vectors are written at all, but if you are drawing a diagram, that's how you'll want to position them.

[@BindhuJBSG]

Is component of b on a is called scalar projection

[@KatePenner]

Yes!

[@kyawmyatlin8364]

j)