Vectors dot product and cross product help

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Homework Statement


Vectors A and B (both with the lines over it) lie in an xy plane. Vector A has magnitude 8 and angle 130 degrees, Vector B has components Bx=-7.72 and By=-9.2.
a)What is 5(vector A) dot vector B?
b)What is 4(Vector A) cross 3(vector B) in unit vector notation and magnitude angle notation with spherical coordinates?


Homework Equations


Vector A dot Vector B=abcos(phi)
Other vector equations that can apply to this that I don't know maybe...

The Attempt at a Solution


I figured that I try to find the vector B by doing the Pythagorean theorem with the two components of B and I get -12 as magnitude. After that I'm not even sure what to do, like for the 5(vector A) do I multiply the angle and magnitude by 5 then do the Vector A dot Vector B=abcos(phi) equation? Same question applies to b and how do I turn the magnitude and the angle into unit vector notation and magnitude angle notation? Thanks in advance.

EDIT: Forget A, I solved it
 
Last edited:

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
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Homework Statement


Vectors A and B (both with the lines over it) lie in an xy plane. Vector A has magnitude 8 and angle 130 degrees, Vector B has components Bx=-7.72 and By=-9.2.
a)What is 5(vector A) dot vector B?
b)What is 4(Vector A) cross 3(vector B) in unit vector notation and magnitude angle notation with spherical coordinates?


Homework Equations


Vector A dot Vector B=abcos(phi)
Other vector equations that can apply to this that I don't know maybe...

The Attempt at a Solution


I figured that I try to find the vector B by doing the Pythagorean theorem with the two components of B and I get -12 as magnitude. After that I'm not even sure what to do, like for the 5(vector A) do I multiply the angle and magnitude by 5 then do the Vector A dot Vector B=abcos(phi) equation? Same question applies to b and how do I turn the magnitude and the angle into unit vector notation and magnitude angle notation? Thanks in advance.

EDIT: Forget A, I solved it

The easiest way to do part b) is to start by finding [tex]A_x[/itex] and [tex]A_y[/itex]. As a hint on finding those components, consider [tex]\vec{A}\cdot\vec{e}_x[/itex] and [tex]\vec{A}\cdot\vec{e}_y[/itex] :wink:
 
  • #3
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Where does the ex and ey come from?
 
  • #4
gabbagabbahey
Homework Helper
Gold Member
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Where does the ex and ey come from?

I'm using them to represent the Cartesian unit vectors. You might be more used to seeing i and j....different authors use different notations for the same quantities, so it's worth familiarizing yourself with common notations.
 

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