MATH200 December 2013
Work in progress: this question page is incomplete, there might be mistakes in the material you are seeing here.
• Q1 (a) i • Q1 (a) ii • Q1 (b) i • Q1 (b) ii • Q1 (b) iii • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 • Q7 • Q8 (a) • Q8 (b) • Q9 (a) • Q9 (b) •
Question 01 (a) ii
The line has vector parametric equation
ii. Let be the angle between the line and the plane given by the equation . Find .
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!
Recall the definition of the dot product:
What does it tell you about two intersecting vectors?
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The line has a directional vector of while the plane has a normal vector of
By the definition of the dot product,
(where is the angle between and )
however, is the angle between and as shown below.
, the angle we're interested in is simply