Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 06
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Question A 06 

Questions A5A6 below involve the vectors and For each question A5A6 below justify your answer with a short computation or a short justification in words. Note that the vector has a constant in the last component. (6) For what value or values of (if any) are and parallel? 
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 

Two vectors and are parallel if and only if we can find a nonzero constant such that 
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. To make the given two vectors and parallel, we need for some nonzero . By comparing the first components, we have . However, from the second components, we get , so that . Therefore, for any value of , there is no nonzero constant to make hold. In other words, there is no value of such that the given two vectors and are parallel. 