Science:Math Exam Resources/Courses/MATH105/April 2018/Question 01 (a)

MATH105 April 2018

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Question 01 (a)
(a) The plane ${\textstyle -x-2y+3z=8}$ intersects the ${\textstyle y}$-axis at the point ${\textstyle P=(a,b,c)}$. Find the values of ${\textstyle a,b}$ and ${\textstyle c}$.

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
Consider simultaneous equations.

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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. The points $(x,y,z)$ on the $y$-axis always satisfy $x=0$ and $z=0$. Therefore, the relevant simultaneous equations are $$-x-2y+3z=8;\;x=0;\;z=0.$$ Plugging the second and third into the first and solving for ${\textstyle y}$ gives ${\textstyle y=-4}$, so the point of intersection is ${\textstyle (0,-4,0)}$. Answer: $\color {blue}a=0,b=-4,c=0.$