LECTURE 2 Basic Vector Arithmetic

PLAN (2 min)

• Scope (tiny): Understand Very basic Arithmetic
• Outputs: CRIBS + 2 questons
• Stop-condition: Solved 1 vector question

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WATCH (10 min) — active capture

S-Q-S per pause (Summary • Question • Sketch note)

• Timestamps:
• Takeaways:

$$Equality=\tilde{b}=\tilde{a}\to EverythingMatches!$$ $$ZeroVector=x_a=0\cap y_a=0thena=(0,0)=\tilde{0}$$ $$Scalar:\tilde{b}=\widetilde{-a}$$ $$Scalardirection:\tilde{b}=r\tilde{a}:\tilde{b}=r(x_a,y_a):(r{x}_a,r{y}_a)$$ $$Addition$$ $$Subtraction$$

• 1 sketch cue: (what to draw / axis / labels)
• Draw addition subtraction notes

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DTS — Deep-Thinking Sprint (15 min)

Fill CRIBS from memory (6–10 lines total).

C — Context (where/why):

• Vectors in $R^n$ model magnitude + direction.
• Vector arithmetic is the backbone for all related topics

R — Relationships (links/checks):

• Magnitude, direction, basic algebra (expanding brackets etc)

I — Intuition (picture/story):

• Think of a bowling ball being rolled. it could be rolled onto another ball with a magnitude, parallel to the ball, or hit a pin thats 0 magntiude.

B — Boundaries (fails/traps):

• Not sure

S — Symbols/Steps (formula/algorithm):

2 self-made micro-examples:

• Ex1

Given $a$ = $(0,1,2)$ and $b$ = $1,2-3$ and $c$ = $3,2,0$ Find $a+2b-c$