Science:Math Exam Resources/Courses/MATH105/April 2016/Question 01 (a)
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Question 01 (a) 

Find an equation of the plane that passes through the point with a normal vector . 
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 the equation of plane when the normal vector and a point on the plane are given? 
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 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. An equation of a plane that passes through the point and is orthogonal to a vector (a normal vector) is given by or by the simplified form where . Here, we have the point and the normal vector . So, the equation of the plane is
which implies
We then get 
Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let be a point on the plane. Then the vector lies on the plane. Since a normal vector on a plane is orthogonal to any vector lying on the plane, we have .
