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Vectors in CSE 681: Basics, Normalizing, Dot & Cross Products

Understand the fundamental concepts of vectors in CSE 681: basics, normalization, dot product, cross product, reflection vector, and parametric equations of a line. Learn how to compute unit vectors, calculate dot and cross products, and use vectors in 3D space.

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Vectors in CSE 681: Basics, Normalizing, Dot & Cross Products

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  1. Brief Review:Vectors CSE 681

  2. Vectors • Basics • Normalizing a vector => unit vector • Dot product • Cross product • Reflection vector • Parametric form of a line CSE 681

  3. Basics • Vectors • Have a direction and a length • Do not have a position in space • Normal vector • Is ‘normal’, or perpendicular, to a surface • Are usually unit-length, also called ‘normalized’ CSE 681

  4. Normalizing a Vector • Compute the magnitude and divide through • Produces a UNIT VECTOR • Aka NORMALIZED VECTOR To normalize (x,y,z) : CSE 681

  5. Dot Product Scalar Product • If A and B are unit vectors, • If A is unit vector, is the length of B projected onto A B a A CSE 681

  6. A AxB Cross Product a Vector Product B • is orthogonal to plane defined by A and B • With length • If A and B are unit vectors, • If B is unit vector, is perpendicular distance from A to B A a B CSE 681

  7. Reflection Vector In 3D, Reflect V about N to make R Assume N is normalized N S S P R V k q q CSE 681

  8. Parametric Equation of Line • P0 is point on line • V is direction of line • Generalizes to any dimension (2D, 3D, etc) • As 0 < u < 1.0, P(u) goes from P0 to P0+V V P0 CSE 681

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