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# vectors and stuff

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Question | Answer |
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Types of error and descriptions | Random error comes from a lot of trials. Systematic error comes from the measurement device because it is *never* accurate enough. Total error is the rms deviation of the random error plus the systematic error. |

How do you determine the actual range of values? | the average plus or minus the total error gives the range |

How do you reduce error with one measurement? | for a pendulum period, record 10 at once. Divide the time and the error by 10 do decrease error and find a closer value. |

How do you indicate unit vectors and how do you use them? | an i, j, or k with a hat, used to multiply by component to determine direction. |

what is the scalar dot product? | It's the two vectors' mags multiplied by the cosine of theta. That equals Ai*Bi + Aj+Bj. |

how do you find the rms deviation? | The square root of ((<x^2>-<x>^2)/(N-1)), where <x> is the average and N is the sample size. |

how do you find percent error? | rms/average * 100 |

cross product | two vectors' mags multiplied by sine of theta. finds shared area of parallelogram. right hand rule determines which side of the paper it is. a bullet in a circle=out of, circle x = into. |

matrices and component form to do cross product | write 3 rows of 6 items. i,j,k,i,j,k, components of "first" vector twice(important), components of second vector twice. Then draw diagonal line to right of i and multiply numbers. Subtract the opposite-facing i line. This is i component. Repeat for j, k. |

difference quotient | (f(a+h)-f(a))/h, h-->0 |

cross product defined= | actually matrix business and 3 components added together, can't tell whether it goes in or out at that point. |