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

I have troubles with dot products.

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

I have troubles with dot products.

Tutors, please sign in to answer this question.

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>|| = √(2^{2} + 2^{2} + 2^{2}) = 2√3.

Larry G.

Algebra/Geometry/SAT Tutor

Bronx, NY

4.9
(142 ratings)

CAROLE C.

Experienced Tutor and Certified College Adviser

Montclair, NJ

5.0
(705 ratings)

Tabitha C.

Fun and Exciting Learning from a New York State Certified Teacher

Bronx, NY

5.0
(616 ratings)