Subjects

Sections | |||
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Review of Vectors vs. Scalars | 2 mins | 0 completed | Learn |

Introduction to Vectors | 7 mins | 0 completed | Learn |

Adding Vectors Graphically | 23 mins | 0 completed | Learn |

Vector Composition & Decomposition | 12 mins | 0 completed | Learn |

Adding Vectors by Components | 14 mins | 0 completed | Learn |

Trig Review | 24 mins | 0 completed | Learn |

Unit Vectors | 16 mins | 0 completed | Learn |

Introduction to Dot Product (Scalar Product) | 12 mins | 0 completed | Learn |

Calculating Dot Product Using Components | 12 mins | 0 completed | Learn |

Additional Practice |
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Vectors in 3D |

Intro to Cross Product (Vector Product) |

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Concept #1: Vector Composition & Decomposition

Example #1: Calculating Magnitude & Components of a Vector

A man is dragging a trunk up the loading ramp of a moving truck. The ramp has a slope angle of 20.0°, and the man pulls upward with a force whose direction makes an angle of 30.0° with the ramp in the figure.(a) How large a force exttip{vec{F}}{F_vec} is necessary for the component exttip{F_{mit x}}{F_x} parallel to the ramp to be 90.0 N?(b) How large will the component exttip{F_{mit y}}{F_y} perpendicular to the ramp then be?

Your neighbor Paul has rented a truck with a loading ramp. The ramp is tilted upward at 35° and Paul is pulling a large crate up the ramp with a rope that angles 30° above the ramp. Paul pulls with a force of 750 N. What is the magnitude of...(a) the horizontal component of his force?(b) the vertical component of his force?

Kami is walking through the airport with her two-wheeled suitcase. The suitcase handle is tilted 40° from vertical, and Kami pulls parallel to the handle with a force of 120 N. (Force is a vector measured in newtons, abbreviated N.) What are the horizontal and vertical components of her applied force?

A position vector in the first quadrant has an x-component of 18 m and a magnitude of 30 m.What is the value of its y-component?

Write each vector in the figure in terms of the unit vectors i and j.

Part A: What is the x-component of vector E of the figure in terms of the angle θ and the magnitude E ? (Express your answer in terms of the variables θ and E )Part B: What is the y-component of vector E⃗ of the figure in terms of the angle θ and the magnitude E ? (Express your answer in terms of the variables θ and E )Part C: For the same vector, what is the x-component in terms of the angle ϕ and the magnitude E ? (Express your answer in terms of the variables ϕ and E )Part D: For the same vector, what is the y-component in terms of the angle ϕ and the magnitude E ? (Express your answer in terms of the variables ϕ and E )

Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured counterclockwise from the positive x-axis.

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