- #1
uchicago2012
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Homework Statement
Write the vectors B,D, and F in the figure in Cartesian form, with unit vectors.
(See attachments)
Homework Equations
ax = a cos theta
ay = a sin theta
where a = magnitude of vector a, and theta = the angle vector a makes with the positive direction of the x axis
The Attempt at a Solution
I'm having trouble with this "the angle vector a makes with the positive direction of the x axis" business. What does that mean, exactly? The smallest angle that the vector can make with the positive direction of the x axis? Because there are two angles it could make, technically. My book is not specific and I'm confused.
In one part of my book it has a note: "Angles that are measured relative to the positive direction of the x-axis are positive if they are measured in the counter clockwise direction and negative if measured clockwise. For example, 210 degrees and -150 degrees are the same angle"
I thought maybe it's just talking about a protractor but then I wondered if it had anything to do with the angle theta business.
So how exactly does one find the angle a vector makes with the positive direction of the x axis?
The thetas I found for the vectors in the images are:
Vector B: 53 degrees
Vector D: 143 degrees
Vector F: I haven't any idea
For Vector B, I arbitrarily decided to use the smaller angle.
For Vector D, I stuck with the smaller angle idea and found theta to be 143 degrees.
For Vector F, I'm puzzled by the addition of the z axis, as our book doesn't have a formula for resolving the vector of a three dimensional vector, or at least we haven't covered it and I haven't found it. I also wonder how I'm supposed to interpret the "the angle the vector makes with the positive direction of the x axis" business on a three dimensional coordinate system.