# I have two vectors: A:{51.031,−102.062,51.031} (|A|=125) B:{2,−4,−1} (|B|=sqrt(21)~~ 4.58) I am trying to find the amount of vec(A) in the vec(B) direction

I have two vectors:

I am trying to find the amount of $\stackrel{\to }{A}$ in the $\stackrel{\to }{B}$ direction, so I used dot product with the coordinate method:
$\left({x}_{1}×{x}_{2}+{y}_{1}×{y}_{2}+{z}_{1}×{z}_{2}\right)$
$\left(\left[2×51.031\right]+\left[-4×-102.062\right]+\left[-1×51.031\right]\right)=459.279$
If the dot product is supposed to find the magnitude of a vector that is pointing in the direction of another vector, how do I get a result that's more than 3 times the length of the longest vector?
What am I doing wrong?
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Branson Perkins
The magnitude of A in B's direction (i.e. the magnitude of the projection of A onto B) is given by $\frac{A\cdot B}{|B|},$ not $A\cdot B.$
You can see that $A\cdot B$ is wrong by units, too, since it has the units of A times B, rather than A. If we situate B on the x-axis, we want $|A|\mathrm{cos}\theta ,$, where $\theta$ is the angle between A and B. Recall that the dot product is given by $A\cdot B=|A||B|\mathrm{cos}\theta ,$ so $\frac{A\cdot B}{|B|}=|A|\mathrm{cos}\theta ,$, which is what we want