Science:Math Exam Resources/Courses/MATH152/April 2012/Question 01 (e)
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Question 01 (e) 

Let be the plane perpendicular to and through the point P=[1,1,0]. Let be the plane through the points A=[1,0,0], B=[1,2,1], C=[0,1,1]. By L, we denote the line of intersection of and . Calculate the volume of the parallelpiped with edges AB, AC, and AP. 
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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

How can we write the volume of a parallelepiped formed by three vectors in terms of a determinant? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The parallelepiped formed by the vectors , and is given by (the absolute value of) the determinant of the three vectors. From 1(a) and 1(c), we have that and so all we need is , Therefore, the volume of the parallelepiped is given by 