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# Vector Equations

### Useful vector equations and practice problems

Question | Answer |
---|---|

What is a vector? | A quantity that has magnitude and direction |

What is a scalar? | A quantity that has only magnitude. |

What is the initial point in a vector is it its compenent form? | (0,0) |

If u (u1,u2) and v (v1,v2) what is u+v? | (u1+v1, u2+v2) |

what is the magnitude of v? | The square root of (v1)squared + (v2)squared |

If r(t) is a position vector for a particle with respect to time what is the velocity vector? | dr/dt=v(t) |

What is the absolute value of v(t) | Speed |

If v(t) is a velocity vector for a particle with respect to time what is the acceleration vector? | dv/dt=a(t) |

If a(t) is the acceleration vector for a particle with respect to time what is the velocity vector? | v(t)=the antiderivative of a(t) + C |

If v(t) is the velocity vector for a particle with respect to time what is the position vector? | r(t)= the antiderivative of v(t) + C |

If u=(7,3) and v=(-2,4) what is u-v ? | (9,-1) |

Write the vector from point P (3,-1) to point Q (2,4) as a linear combination | (-1,5) -1i+5j |

v(t)=(5t)i + (tsquared)j what is r(t)? | r(t)=(5/2tsquared + C)i + (1/3tcubed + C)j |

If r(t)= (ln(t)+1)i + (tsquared-1)j, find the distance traveled from t=0 to t=2 | L=antiderivative of the square-root of (1/(1+t))squared + (4t)squared = 4.335 |

Created by:
weier1