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Angle between two vectors given their scalar product and magnitude of their vector pr

  • Thread starter nabelekt
  • Start date
  • #1
6
0

Homework Statement



Vectors and have scalar product -7.00 and their vector product has magnitude 3.00.
What is the angle between these two vectors?

Homework Equations



|A| |B| cosθ = -7
|A| |B| sinθ = 3

The Attempt at a Solution



tanθ = (-3/7)
tan-1(-3/7)=θ

When I enter tan-1(-3/7) into my calculator, I get -23.199, but when I enter 23.199 into MasteringPhysics, it tells me that I am incorrect. What am I doing wrong?

Thanks!
 

Answers and Replies

  • #2
6,054
390


Is the angle expected in degrees or radians?
 
  • #3
6
0


The answer is required to be in degrees.
 
  • #4
6,054
390


What is the range of arctan? From the given values, can you determine whether the angle is really in that range?
 
  • #5
6
0


I believe that the range of arctan is 270°<θ<90°. Correct? 23.199° seems to be in that range…

Thanks for the help. It's been a while since I've done this stuff.
 
  • #6
CAF123
Gold Member
2,889
88


The range given does not make sense. The range should be (-π/2,π/2).
 
  • #8
6
0


I guess it would actually lie in quadrant II whereas the range of arctan is quadrants I and IV. So what should I do?
 
  • #9
6,054
390


You should express you angle via some auxiliary angle that is in the range of arctan, obtain the value of the auxiliary angle, and then get your angle.
 
  • #10
gabbagabbahey
Homework Helper
Gold Member
5,002
6


Homework Statement



Vectors and have scalar product -7.00 and their vector product has magnitude 3.00.
What is the angle between these two vectors?

Homework Equations



|A| |B| cosθ = -7
|A| |B| sinθ = 3

The Attempt at a Solution



tanθ = (-3/7)
tan-1(-3/7)=θ

When I enter tan-1(-3/7) into my calculator, I get -23.199, but when I enter 23.199 into MasteringPhysics, it tells me that I am incorrect. What am I doing wrong?

Thanks!
You should take care to notice two things here:

(1) If |A| |B| cosθ = -7, then cosθ must be negative. In which quadrants is cosθ negative?

(2) tanθ has a period of ∏ radians, so tanθ = tan(θ+n∏) for any integer n, and tan-1(tanθ) = θ +n∏. Can you find a value of n that gives you an angle in the correct quadrant for θ +n∏=tan-1(-3/7)?
 

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