Angle between vectors (2,1,-4) and (-3,0,1) using dot product formula

[philo51]

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?

 

[quasar987]

absA = $\sqrt{21}$, not 21

 

[philo51]

that still isn't right?

 

[HallsofIvy]

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 $$\theta= cos^{-1} \frac{-10}{\sqrt{210}}$$.

 

[philo51]

no i realized that i just multiplied weird.. sorry thanks!