Math Hacks: Vectors - What are Vector Projections?

#shorts

In this video, we are covering the question, what are vector projections? We use vector projections in the definition of dot product, but they are a unique concept themselves!

Vector projections are formed by "projecting" one vector (Vector A) onto another (Vector B)! To do this, we break Vector A into two components, one parallel to Vector B, and one perpendicular to Vector B! The vector projection is just the parallel component! Now if our two vectors are perpendicular to each other, there is actually no projection that we can create!

Now the magnitude of the vector projection is |A|cos(theta) which we can solve for using the magnitude of Vector A and the angle (theta) between our two vectors, but a vector must have both a magnitude and a direction! To get the direction, we just multiply the magnitude by the unique vector of Vector B! This unit vector has a magnitude of 1, so won't change the magnitude we just calculated, but will provide us with the direction for out projection!

For additional videos on vectors, check out my playlist below:

[vintoncerf]

a better explanation than 30-minute-long videos thank

[olaftaczkowski]

its amazing that a youtube short explained this better then a 30min vid from my prof thx bro

[RuthBereket-twpj]

I am here in oct. 2024 thank you sir your videos are very useful😊😊

[nubiairasema]

How the heck did I learned more from a YouTube reel than my university professor

[rituraj]

damn the voice !!! btw explained very nicely . thanks

[yaboi]

can you do one for the perpendicular vector

[Tardigreat.]

Hello, I have a question...

When providing the definition you use projb a, but when explaining the problem with the diagram you use proja b.

Why wouldn't the diagram use projb a?

[shashwatsen]

Dot product gives projection
Cross product gives area














1, 5epoxypentane gives😳