Byron S. answered • 10/29/14

Math and Science Tutor with an Engineering Background

**u · v**

**u**= ⟨x, y, z⟩ and

**v**= ⟨1, 2, 5⟩

**u · v**= |

**u**| |

**v**| cos θ where θ is the angle between the vectors

**u**is a unit vector, it has magnitude 1.

**v**has magnitude √(1

^{2}+2

^{2}+5

^{2}) = √(30)

**u**| |

**v**| cos θ

**u**and

**v**are in opposite directions.

**v**= ⟨-1, -2, -5⟩

**u**= -

**v**/|

**v**| = ⟨-1/√(30), -2/√(30), -5/√(30)⟩

Byron S.

10/29/14