Two vectors $\vec A$ and $\vec B$ are given by $\vec A = 5\hat i + 6\hat j + 7\hat k$ and $\vec B = 3\hat i- 8\hat j + 2\hat k$. If these two vectors are drawn starting at the same point, what is the angle between them?

Question

anonymous · Answer

use dot product formula...

anonymous · Answer

A . B= A B Cos(theta)

lgbasallote · Answer

can't i just use something simple like $$\tan^{-1} \left (\frac yx\right)$$

anonymous · Answer

what's y and x here?

lgbasallote · Answer

i have no idea....well i also tried getting the value of vector A and B...

lgbasallote · Answer

can i find out the answer using those info?

anonymous · Answer

actually if a vector R = x i + y j then theta is the the angle make by vector with x-axis

anonymous · Answer

which u wrote theta = arc tan(y/x)

anonymous · Answer

yeah to find A use the dispacement formula. thats root(i²+j²+k²)

lgbasallote · Answer

yes...so if i have A and B...what can i do next?

lgbasallote · Answer

im pretty sure it's not $$\tan^{-1} \left (\frac BA \right)$$

anonymous · Answer

A . B= A B Cos(theta)...use this...LHS is the dot product of vector A and B

anonymous · Answer

and On RHS ... A and B are the magnitudes of vectors A and B

lgbasallote · Answer

A and B are the values of A and B i found?

lgbasallote · Answer

the ones without the i j and k?

anonymous · Answer

lhs = 5.3+6.(-8)+7.2

lgbasallote · Answer

uhh where did these numbers come from?

anonymous · Answer

then use the cosine law 
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