Vectors Tip or head: D Tail: C

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Presentation transcript:

Vectors Tip or head: D Tail: C Vector 𝐶𝐷 is NOT equivalent to vector 𝐷𝐶

Vectors

Vectors Example: 𝑢 = <4, −2> Notation: <𝑢 1 , 𝑢 2 > <𝑢 𝑥 , 𝑢 𝑦 > Draw equivalent vectors Find its length, magnitude, norm, or absolute value

Operations with Vectors: addition 𝐴𝐵 + 𝐵𝐶 “Tip to tail” 𝐵𝐶 + 𝐵𝐴 ???

Operations with Vectors: addition 𝒖= <3,−2> 𝒗= <−4,−6> 𝒖+𝒗=

Operations with Vectors: scalar multiplication How do 𝟓 𝒗 and 𝒗 compare? 𝑣 = <3,2> 5 𝑣 = − 𝑣 =

Operations with Vectors: scalar multiplication How do − 𝒗 and 𝒗 compare? 𝑣 = <3,2> 5 𝑣 = − 𝑣 =

Operations with Vectors 𝑢 =<3,−2> 𝑣 =<−4,−2> 3 𝑢 −6 𝑣 =

Unit Vectors

Unit Vectors: rewrite 𝑢 = <3, 2> In general:

Unit Vectors: rewrite 𝒗= <4, 11,−5> =

Unit Vectors Write a unit vector with the same direction as 𝒘= <−2, 5>