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

Janessa Benson

Janessa Benson

Answered question

2022-09-06

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 ] ) = 459.279
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?

Answer & Explanation

Branson Perkins

Branson Perkins

Beginner2022-09-07Added 7 answers

The magnitude of A in B'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

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