Find the area of the parallelogram?

Question

Find the area of the parallelogram spanned by the vectors <1, 0, -1> and <-2, 2, 0>.

I have troubles with dot products.

Answer 1

This one is actually a classic problem for cross products.

<1, 0, -1> × <-2, 2, 0>

      |  i     j    k  |

=    |  1    0   -1 |

      | -2    2    0 |

= <0*0 - (-1)*2, (-1)*(-2) - 1*0, 1*2 - 0*(-2)>

= <2, 2, 2>

Area = ||<2,2,2>|| = √(2² + 2² + 2²) = 2√3.