Vectors

Vectors

1. Using vectors to write equations in 3 space

   • equation of a line using a direction vector
   • equation of a plane using a normal vector and a point
     • a(x-x0)+b(y-y0)+c(z-z0)=0
   • normal vector
     • vector perpendicular to a plane

2. magnitude and direction

   • magnitude by pythagorean theorem of x and y components
     • direction by

3. multiplying vectors

   • by a scalar
     • stretch or compress
   • dot product (scalar result)
     • a · b = |a| × |b| × cos(θ)
     • a · b = ax × bx + ay × by
       • include z-components for 3-space
     • smallest at 90 degrees and largest at 0 or 180 degrees
   • cross product
     • produces third vector at 90 degree angle in 3-space
       • a × b = |a| |b| sin(θ) n
     • smallest at 0 and largest at 90

4. two space and three space

5. addition and subtraction of vectors

   • tip to tail addition
   • reverse direction for subtraction

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