Find Angle Between Avec and Bvec: Rads Formula Explained

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The discussion focuses on calculating the angle between two vectors, A(vec) and B(vec), using the formula A(vec)·B(vec) = |A| |B| cos(θ). The user initially miscalculated the magnitudes of the vectors, stating |A| as 21 instead of √21 and |B| as 10 instead of √10. After clarification, the correct approach involves using θ = cos^(-1)(-10/√210) for the angle calculation. The conversation highlights the importance of accurately determining vector magnitudes in trigonometric calculations. Ultimately, the user acknowledges their error in multiplication and thanks the participants for their assistance.
philo51
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A(vec)=(2,1,-4) B(vec)=(-3,0,1) C(vec)=(-1,-1,2)

whats the angle between Avec and Bvec in rads.

i know the formula

A(vec)*B(vec)= abs(A)*abs(B)*cos(theta)

A(vec)*B(vec)=-10

so why won't cos^-1(-10/(21)(10)) work?
 
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absA = \sqrt{21}, not 21
 
that still isn't right?
 
What still isn't right?

You were told that the length of vector A is \sqrt{21}, not 21.

Did it then occur to you that the length of vector B should be \sqrt{10}, not 10?

Try \theta= cos^{-1} \frac{-10}{\sqrt{210}}.
 
no i realized that i just multiplied weird.. sorry thanks!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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