Area of a parallelogram using determinants

[cse63146]

Homework Statement

let v = (1,0,1) and u = (0,2,1)

Find the area of the parallelogram {sv + tu : 0 <= s, t <=1)

Homework Equations

The Attempt at a Solution

I know the area of a parallelogram is the determinant of a 2x2 matrix, but they gave v and u in R^3. Would I just ignore the z component in this case?

 

[missbooty87]

technically there is a 3rd vector which could be r = (0,0,0)

and NEVER ignore any component given in a question like this :P

So, let the origin = r therefore find the vectors rv and ru
Then, find the magnitude of the cross product of the two vectors, rv and ru
i.e. |rv x ru|
Your answer should be the Area of the Parallelogram. The Area of a Triangle formed in vectors is HALF the Parallelogram.

I hope I've been helpful.

missbooty87

 

[cse63146]

I could be wrong but isn't (0,0,0)(1,0,1) = 0?

 

[missbooty87]

I could be wrong but isn't (0,0,0)(1,0,1) = 0?

yes... But how is that relevant to your question... i said find the two new vectors and then cross multiply the two new vectors he he... not multiply or cross-multiply the individual vectors he he...

And if I wasn't clear let me rephrase.
--------------------
1st step:

find the two new vectors

the first vector is from R to V (i.e. From the Origin to the vector v)
the second vector is from R to U
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2nd step:

Cross multiply the RV and RU (i.e. |RV x RU|)
--------------------
3rd step:

Claim that you have the answer
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If you don't understand let me know.