Dot Product of Two Vectors

This physics and precalculus video tutorial explains how to find the dot product of two vectors and how to find the angle between vectors. The full version of this video explains how to determine if two vectors are orthogonal / perpendicular, parallel, or neither using the dot product formula and by analyzing the slope. It also explains how to find the scalar projection and the vector projection of v onto w.
Full 2 Hour 23 Minute Video on Patreon:
/ mathsciencetutor
Direct Link to The Full Video:
bit.ly/3yuhE39
Vectors - Free Formula Sheet:
bit.ly/3WYIGOv
________________________
Full Video - TH-cam:
• Dot Product of Two Vec...
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[@TheOrganicChemistryTutor]

Vectors - Free Formula Sheet: bit.ly/3WYIGOv
Full 2 Hour 23 Minute Video: www.patreon.com/MathScienceTutor
Direct Link to The Full Video: bit.ly/3yuhE39

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[@eggxecution]

if you're confused why i, j, k, disappeared, it's because they're "vectors" not imaginary number symbols with a value of sqrt(-1). Vectors if you multiply the same vectors you get 1. For example: ixi =1, jxj =1, kxj = 1. If you multiply the vectors that are not the same all of it will = 0. I got confused too before lol so I'm writing this down.

[@pearleunjoo5439]

Yeah yeah I think the main point is i, j & k are vectors, NOT imaginary numbers like a,b,c,x,y,z etc. He should have used this sign “^” on i, j & k. I am confused why he didn't. Also, another mistake at 12:03...Do u notice it too?

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I'm currently not looking at the dot product or vector calculations in my role (Project Mgmt, Statistics), but this was a great 35 min refresher. Thank You!!

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[@mandemskullmail700]

think you made a mistake with the notations at 12:05. it should be (ax^2 ; ay^2; az^2) and not (bx^2; cx^2)

[@pearleunjoo5439]

Yep you are right. I noticed it too. Glad that someone also noticed.

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I have a question. First of all, thank you so much sir for this. How do we know whether a vector is in quadrant 1,2,3 or 4?

[@kianooshbaghi6754]

The signs of the x and y components tells you where it is situated.

[@foshcat1885]

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[@pearleunjoo5439]

12:03
I think a little mistake happened here..... It would be
|a| = √(ax²+ay²+az²)
You wrote bx² instead of ay² & cx² instead of az² :")

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What about the direction of the resultant vector

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Please in 20:25 why did you not use the negative 4?

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Why did u remove negative sign from tanx=-4/5 when searching for angle b

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What is the angle between vector A and Z axis?

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I don't get it when he say ignore the negative sign of tangent.... Because during the problem we have done so far, negative sign of these are crucial for solving an angle....could anyone explain it to me??

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