Science:Math Exam Resources/Courses/MATH105/April 2015/Question 01 (a)
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Question 01 (a) 

Find an equation of the plane parallel to the plane passing through the point 
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 

What is a normal vector to the given plane? What is a normal vector of the plane you are looking for? Given a normal vector and a point, finding the equation of the plane follows a simple formula. 
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. For a plane parallel to , we can take its normal vector to be (two parallel planes have normal vectors that are scalar multiples of each other, so without loss of generality we may assume their normal vectors are identical). Thus, the plane we seek has equation where is any point on the plane. We are told that the plane passes through so we take , , and to obtain: , or equivalently, . 