Find the angle θ between the vectors.?
u = 2cos(2π/3) i + 2sin(2π/3) j
v = 5cos(π/4) i + 5sin(π/4) j
θ=_________________
cos(2pi/3)=-1/2
sin(2pi/3)=root3/2
sin(pi/4)=cos(pi/4)=1/root2
substitute the values.
-1 i + root3 j
and
5i+5j
-------
root2
take dot product of the two vectors and divide it by the magnitude of the individual vectors.
A.B= abcos(θ)
where A n B are the vectors and a n b are the magnitudes.
here A.B=-5/root2 + 5.root(3/2)
= 5(root3 - 1)/root2
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Answers & Comments
cos(2pi/3)=-1/2
sin(2pi/3)=root3/2
sin(pi/4)=cos(pi/4)=1/root2
substitute the values.
-1 i + root3 j
and
5i+5j
-------
root2
take dot product of the two vectors and divide it by the magnitude of the individual vectors.
A.B= abcos(θ)
where A n B are the vectors and a n b are the magnitudes.
here A.B=-5/root2 + 5.root(3/2)
= 5(root3 - 1)/root2