Science:Math Exam Resources/Courses/MATH200/April 2012/Question 01 (b)
• Q1 (a) • Q1 (b) • Q2 (a) • Q2 (b) • Q3 • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 • Q8 • Q9 • Q10 •
Question 01 (b) 

Let L be the line which is parallel to the plane and perpendicular to the line Find parametric equations for the line L if L passes through a point Q(a,b,c) where a<0, b>0, c>0 and the distances from Q to the xyplane, xzplane, and the yzplane are 2, 3, and 4 respectively. 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

From part (a) we know that the direction vector of the line is

Hint 2 

Recall that the distance of a point
to the plane is the absolute value of the coordinate . 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. To find the line to the line , we must find such that the point has distance to the plane. This means . Since , we have . The distance from to the plane is , hence . With , we have . The distance from to the plane is , hence . With , we have . Hence and . 