I have two vectors: A : { 51.031 , − 102.062 , 51.031 } ( | A | = 125 ) B : { 2 , − 4 , − 1 } ( | B | = 21 ≈ 4.58 )I am trying to find the amount of A → in the B → direction, so I used dot product with the coordinate method: ( x 1 × x 2 + y 1 × y 2 + z 1 × z 2 ) ( [ 2 × 51.031 ] + [ − 4 × − 102.062 ] + [ − 1 × 51.031 ] ) = 459.279If 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?

Question

I have two vectors:  A  :  {  51.031  ,  −  102.062  ,  51.031  }     (      |    A      |    =  125  )  B  :  {  2  ,  −  4  ,  −  1  }     (      |    B      |    =      21    ≈  4.58  )I am trying to find the amount of             A      →        in the             B      →       direction, so I used dot product with the coordinate method:  (      x    1    ×      x    2    +      y    1    ×      y    2    +      z    1    ×      z    2    )  (  [  2  ×  51.031  ]  +  [  −  4  ×  −  102.062  ]  +  [  −  1  ×  51.031  ]  )  =  459.279If 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&#039;s more than 3 times the length of the longest vector?What am I doing wrong?

Branson Perkins · Accepted Answer

The magnitude of A in B&#039;s direction (i.e. the magnitude of the projection of A onto B) is given by             A      ⋅      B                      |            B              |              , not   A  ⋅  B  .You can see that   A  ⋅  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      |    cos  ⁡  θ  ,, where   θ is the angle between A and B. Recall that the dot product is given by   A  ⋅  B  =      |    A      |        |    B      |    cos  ⁡  θ  , so             A      ⋅      B                      |            B              |              =      |    A      |    cos  ⁡  θ  ,, which is what we want

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

Answered question

Answer & Explanation

New Questions in Precalculus