cross product vectors

[dusky bane]

Hello can someone check my part c with the use of the cross product

[hollow crypt]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[granite apex]

Hey there Jessica!

This question is a multi-step question.

a) What is PQ? Point Q - Point P right?
So we have -6i + 3j or [-6, 3] as a vector.

b) QR = [9, 18]
QR dot PR is zero, so thus 90 degrees. This can be useful (but optional) because we can use the formula:
|a x b| = |a| * |b| sin90
|a x b| = |a| * |b|

c) PS = 3QR = [27, 54]
We are missing a vector PR to do cross product with PS. However:
PR = PQ + QR
= [-6, 3] + [9, 18]
= [3, 21]

So we have everything we need to do cross product:
PS = [27, 54], PQ = [3, 21]
QP = -PQ = [6, -3], QR = [9, 18] (here is 90°)

Area = (|PS x PQ| + |QP x QR|)/2

Your solution is correct in the end!