Finding the angle between 2 vectors

[PinkFlamingo]

Could someone refresh my memory how to find the angle between 2 vectors in 3d, say:

a= 4i + j + 2k
b= -i +2j + k

Thanks!

 

[enigma]

dot product

a.b = |a||b|cos (ang)

 

[PinkFlamingo]

So how would I find the angle for the two I posted?

 

[cookiemonster]

He just told you. Solve for theta and plug and chug.

$$\theta = \arccos{\left( \frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|\right)}$$

$$\vec{a}\cdot\vec{b} = a_1b_1 + a_2b_2 + a_3b_3$$
and
$$|\vec{a}| = \sqrt{{a_1}^2 + {a_2}^2 + {a_3}^2}$$

if $\vec{a} = <a_1,a_2,a_3>$ and likewise for b.

cookiemonster

 

[Ebolamonk3y]

Nice thinking Cookieman...

 

[PinkFlamingo]

Thank you!