Science:Math Exam Resources/Courses/MATH152/April 2022/Question A05
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Question A05 

Find the volume of the parallelepiped with sides , where 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

First, you need to compute . One way to do this is via the mnemonic 
Hint 2 

Second, recall that the crossproduct of two vectors is orthogonal to both vectors and its norm is the area of the parallelogram spanned by the two vectors. Try sketching these vectors. 
Hint 3 

For a different approach, you might remember that the volume of a parallelepiped that is spanned by the 3dimensional vectors is equal to 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. By the first hint, we have By the second hint, the parallelepiped in question is a prism whose base has area , and whose height has length , so its volume is 
Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. We provide the solution that follows the third hint. For that, we still need the computation By the second hint, the volume of the parallelepiped is 