__Question 7.4__:
Show that the area of the triangle contained between the vectors

**a**and**b**is one half of the magnitude of**a**×**b**.

__Solution__:Consider two vectors

**OK = a**and

**OM = b**, inclined at an angle

*θ*, as shown in the following figure.

In
ΔOMN, we can write the relation:

Sin θ = MN / OM = MN / |

MN = |

= 2 × Area of ΔOMK

∴ Area of ΔOMK = (1/2) |

Sin θ = MN / OM = MN / |

**b**|MN = |

**b**| Sin*θ**|***a**X**a**| = |**a**| |**b**| Sin*θ**= OK X MN X 2 / 2*= 2 × Area of ΔOMK

∴ Area of ΔOMK = (1/2) |

**a**X**b**|
## No comments:

## Post a Comment