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Vector Operations Physics Ch.3 sec 2 Pg. 88-97

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2-Dimensional vectors Coordinate systems in 2 dimensions

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2-Dimensional vectors Use right triangles to determine resultant magnitude and direction

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2-Dimensional vectors Pythagorean theorem - finding length of sides of a right triangle a 2 + b 2 = c 2 Δx 2 + Δy 2 = D R 2 a, b, & Δx, Δy are the side / legs of the triangle c and D R are the hypotenuses D R = Resultant displacement

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2-Dimensional vectors a b ΔyΔy ΔxΔx c DRDR Θ Θ

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Θ = angle between two vectors(theta) (including direction) a, b, & Δx, Δy are the side / legs of the triangle c and D R are the hypotenuses D R = Resultant displacement

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Resolving vectors into components Trigonometric Functions Sin Θ = Opposite Hypotenuse CosΘ = Adjacent Hypotenuse TanΘ = Opposite Adjacent

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2-Dimensional vectors Use tangent to find direction of resultant Tangent of angle = opposite leg adjacent leg

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Resolving vectors into components Components of a vector – projections of a vector along the axes of coordinate system X component Y component Every vector can be broken into x & y component (2D)

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Resolving vectors into components V R 2 = V x 2 + V y 2 V y = V R (sin Θ) V x = V R (cos Θ) **D can be substituted for V when using displacements

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