math - Determine the distance of a Vector 3 along another Vector 3 -

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i have 2 3d vectors. (objects x, y , z float values)

in diagram below, determine length of green line. distance along vector 1 vector 2 is. or, distance origin end of line on vector 1 @ 90' vector 1 , passes thorough point @ end of vector 2.

enter image description here

i doing in unity3d have access quite few helper methods enable me length of vector3 , on easily.

the length obviously

norm(v2)*cos(angle(v1,v2))

and since

cos(angle(v1,v2))=abs(dot(v1,v2))/norm(v1)/norm(v2)

the final formula is

abs(dot(v1,v2))/norm(v1)

one 

e1 = v1/norm(v1)

is unit vector in direction of v1, , green vector is

dot(e1,v2)*e1

resulting in same length formula.


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