Science:Math Exam Resources/Courses/MATH152/April 2022/Question A09
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Question A09 

Find a constant such that the plane defined by is parallel to the line 
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 

The line is given as an intersection of two planes. Can you use the equations of the two planes to find a vector that is parallel to the line? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The planes defining the line have normal vectors . Their crossproduct yields a vector that is parallel to : For this latter vector to be parallel to the plane given by , it must be orthogonal to the vector that is normal to the plane, namely In other words, we have for which the solution is 