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Home Q & A Board Science-Related Homework Help Physics
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rizabove rizabove
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11 years ago
If I have the components of two vectors, let's say vectors A  and B, how do I find the angle between them?

Bx = -9.9
By = -6.6
Ax= -4.2
Ay=+4.6

I need to see the work on this. I think that the x and y refer to how one would plot the vectors, but I don't know how to go from that to the math. Thanks.
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wrote...
#1
11 years ago
one way you could do it would be to calculate the angle between each vector and a common reference axis then just find the difference between the angles (equivalent to converting to polar notation and noting the difference in angle)
wrote...
#2
11 years ago
B=-9.9i-6.6j
A=-4.2i+4.6j
A.B=(-4.2x-9.9)+(-6.6x4.6)
A.B=41.58-30.6
A.B=11(approx)
modA=(-9.9^2+-6.6^2)^1/2
modA=(98.01+43.56)1/2
modA=11.9
modB=(-4.2^2+4.6^2)^1/2
modB=(17.64+38.4)^1/2
modB=7.5
modA.modB=A.B.cosp
modA.modB=11.9x7.5xcosp
modA.modB=A.B=89.25xcosp
cosp=11/89.25
cosp=0.1232
p=82.9deg
wrote...
#3
11 years ago
The angle, measured from the x axis would be atan( y/x)
so vector B would have an angle of atan ( -6.6 / -9.9)  = 33.7 degrees.
But they are both negative so the angle must be in the third quadrant.
i.e 180 + 33.7degrees.  213.7


And for A
atan ( 4.6 / -4.2)  = - 47.6 degrees
But the angle is in the second quadrant.  ( x is negative, y positive)
so it is 180 - 47.6 = 132.4

Finally the angle between the two is found by simple subtraction.
( 213.7 - 132.4 = 81.3 degrees
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