## Vector Algebra |

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### Contents

Vector and Scalar quantities 1 Addition of vectors 3 | 3 |

Multiplication of a vector by a scalar 5 Resolution of a vector | 13 |

Products of two vectors 30 68 | 30 |

Multiple Products 69 96 | 69 |

Vector Equations of a Line and a Plane 97 126 | 97 |

Further Application of Vectors to Geometry and Mechanics 127 192 | 127 |

Geometry of the Sphere | 161 |

The vector equation of a sphere 161 Tangent plane at a given point | 168 |

Application to Mechanics | 175 |

Lamis Theorem 177 Work 183 Vector moment or Torque 184 | 184 |

### Common terms and phrases

a x b ABCD Agra Allahabad b x c bisect bisector Calcutta centre centroid collinear concurrent coplanar diagonals direction cosines displacement dot product Equating the coefficients Find the equation find the vector four points given plane given point given vectors Hence i j k Kanpur length Let the equation line joining line of action line of intersection linear combination linearly locus Lucknow magnitude Marathwada Meerut middle point modulus mutually perpendicular Nagpur null vector opposite edge origin of vectors parallel parallelogram particle plane containing plane passing point G point of intersection polar plane position vector Putting the value quadrilateral required plane respectively resultant Rohilkhand scalar product scalar triple product scalarly shortest distance Show sides Similarly Solution Solved Examples Ex sphere square straight line tetrahedron three non-coplanar vectors three vectors unit vector vector area vector equation vector product velocity vertices Vikram