SOLUTION: Two vectors a and B have components in arbitrary units ax=3.2, ay= 1.6, bx=0.50, by=4.5 a) find the angle between a and B b) Find the components of a vector C that is perpendicul

Question 1206234: Two vectors a and B have components in arbitrary units ax=3.2, ay= 1.6, bx=0.50, by=4.5
a) find the angle between a and B
b) Find the components of a vector C that is perpendicular to a and is in the x-y plane, and has magnitude of 5.0 units
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
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Two vectors a and B have components in arbitrary units ax=3.2, ay= 1.6, bx=0.50, by=4.5
a) find the angle between a and B
b) Find the components of a vector C that is perpendicular to a and is in the x-y plane,
and has magnitude of 5.0 units
~~~~~~~~~~~~~~~~~~~

We are given vectors A and B (both letters are CAPITAL).

    A = (Ax,Ay) = (3.2,1.6),  B = (Bx,By) = (0.5,4.5).


To find the angle  between vectors A and B, use the cosine formula 
via the scalar product of the vectors


     =  =  = 0.54325  (rounded).


So,   = arccos(0.54325}}} = 0.99649 radians = 57.095 degrees  (rounded).

Solved.

----------------

From my post, learn BOTH

    (a)  how to solve the problem, and 

    (b)  how to write vectors and their components consistently.

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