Science:Math Exam Resources/Courses/MATH152/April 2015/Question B 3 (c)
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Question B 3 (c) 

Line and plane shown in the figure are given in parametric form as where

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 

Like in part (a), convert this problem into a system of linear equations, then use the solution(s) to parametrize the intersection. 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. We have
and
for some , , and from the question and part (b). It is easy to see that the line is just the intersection of plane , i. e., any point on the line has to satisfy both equations. Thus we have following equation for line . . Now let's find out the relation among parameters . The first coordinate shows , while the third shows . Summing these equations gives , hence . Substituting it back gives: for any point on line it satisfies
which has is equivalent equation form; for any point on the line satisfies
