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

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

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

Joke for the day: How did the insane asylum inmate escape through the woods?

He took the psycho-path!

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

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

Why do we use absolute value?

Because absolute value is distance from zero!

(2,5)

(4,2)

*

v = (2,-3)

Use exact value.

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

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

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)