6.02 - Relations btw Vectors | High School

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High School
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High School Physics
Academic year:

2024
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6.02 Relationships between Vectors Unit Vectors: ◼ Magnitude is 1 unit v B Zero Vectors: 10cm 10cm 50o ◼ Magnitude is 0 units (a point) 50o A Equivalent or Equipollent Vectors: Same magnitude ◼ Same direction ◼ Same components ◼ Ex. B ◼ v 10cm 10cm 50o 50o A AB = v AB  v Opposite Vectors: Same magnitude ◼ Parallel BUT opposite direction ◼ Components have opposite signs (a, b ) = (− a, − b ) ◼ Notation: AB = − BA or v = − v ◼ B ◼ Ex. v A AB = (2, 6) v = (-2, -6) Collinear or Linearly Dependent Vectors: Same direction or opposite *this also works for opposite ◼ For vectors (a,b) and (c,d), vectors* components follow: ad − bc = 0 ◼ Magnitudes are multiples of one another v = (6,10 ) ◼ Ex. u = (3, 5)   u =K v & ◼ u v Orthogonal Vectors: Perpendicular to each other ◼ Components follow: ac + bd = 0 ◼ ◼ Ex. u = (1, − 2) *look at the slope of each vector* slope1 x slope2 = -1 Ex. (0, 3) v (5, 6) v = (4, 4 ) u = (− 6, 6) v = (2,1) (1, 2) u (6, -3) ◼ Ex. Equivalent: A 326o D AB & EF 2.7 4 B Opposite: 146o C AB & GH H E 326o 2.7 2.7 F 236o I 3.2 J EF & GH 146o G Collinear: AB , CD , EF , GH Orthogonal: IJ & AB CD GH EF ◼ Ex. w = (4,−6) u = (− 2, 3) n = (− 6,12 ) Equivalent: none Opposite: t = (2, − 8) v = (− 4, 6) s = (− 1, 4) m = (2, − 3) r = (2,1) w&v u&m Collinear: t&s m& w&u &v Orthogonal: r &n Visions 2 ◼ Pg 23: #3, #10c, #12 ◼