Science:Math Exam Resources/Courses/MATH105/April 2012/Question 08 (i)
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Question 08 (i) 

Shortanswer question! No credit will be given for the answer (even if it is correct) without the accompanying work. Find the equation of the plane parallel to 3xy+4z=13 passing through the point (2,1,1). 
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 and we can just as well choose their normal vectors to be identical). Thus, the plane we seek has equation where is any point on the plane. We are told the plane passes through so we take , , and and the plane's equation is: or equivalently, . 