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1-10-14(A) & 1-13-14(B) 12.2a Algebraic Representation of Vectors

1-10-14(A) & 1-13-14(B) 12.2a Algebraic Representation of Vectors. Joke for the day: How did the insane asylum inmate escape through the woods?. He took the psycho-path!. Active Learning Assignment?. LESSON: Given the following vector, can we find the vertical and horizontal components?.

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1-10-14(A) & 1-13-14(B) 12.2a Algebraic Representation of Vectors

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  1. 1-10-14(A) & 1-13-14(B) 12.2a Algebraic Representation of Vectors Joke for the day: How did the insane asylum inmate escape through the woods? He took the psycho-path!

  2. Active Learning Assignment?

  3. LESSON: Given the following vector, can we find the vertical and horizontal components? (2,5) AB = (2,-3) * (4,2) v = (2,-3) (Terminal minus initial!!!!) 2 and -3 are the components of AB; AB can be expressed as v

  4. AB = (-5, 1) Try: Given A(8,-5) and B(3, -4), express AB in component form. B – A = (3, -4) – (8, -5 ) Restate = ( 3 – 8 , -4 – (-5) ) Operate Simplify

  5. Why do we use absolute value? Because absolute value is distance from zero! (2,5) (4,2) * v = (2,-3) Use exact value.

  6. AB = (5, – 3) AB = (– 19, – 3) Ex.: Given A(4,2) and B(9, – 1), express AB in component form and find the magnitude of |AB| Try: Given A(7,-3) and B(-12,-6), express AB in component form and find the magnitude of |AB| B – A B – A Restate = (9, – 1) – (4, 2) = (– 12, – 6) – (7, – 3) Operate = ( 9 – 4 , – 1 – 2 ) = (– 12 – 7 , – 6 – (– 3 ) Simplify Magnitude

  7. Vector Operations with Coordinates Given v = (a,b) and u = (c,d), then: Vector Addition: v + u = (a,b) + (c,d) = (a+c , b+d) Vector Subtraction: v – u = (a,b) – (c,d) = (a – c , b – d) Scalar Multiplication: kv = k(a,b) = (ka , kb) (ka , kb) (a+c , b+d) d u v + u kv kb c v v b b a a ka

  8. Given vectors u = (1, – 3) and v = (2,5), find: • u + v b) u – v Restate (1, –3) + (2,5) (1, –3) – (2,5) Operate (1 + 2 , –3 + 5 ) (1 – 2 , –3 – 5 ) Simplify (3, 2) (–1, –8) c) 2u – 3v d) | 2u – 3v| Scalar Multiple Abs. value = Mag. = Distance Formula 2*(1, –3) – 3*(2,5) (2,-6) – (6,15) (2 – 6 , –6 – 15 ) (–4, –21)

  9. Active Learning Assignment: P 429: 1-4, 9,10

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