Why do we need projection of vectors

[parshyaa]

I know that projection of vector B on A is ||B||cos(theta) where theta is the angle between vector A and B . But why do we find it . Is there any application for this

 

[houlahound]

it is useful in many applications when you want to know the parallel contribution of B to the total, eg in resolving a force or calculating work ie;

work = Force X distance in direction of motion

 

[parshyaa]

Ohkkk , thanks

it is useful in many applications when you want to know the parallel contribution of B to the total, eg in resolving a force or calculating work ie;

work = Force X distance in direction of motion

k

 

[houlahound]

read here from

https://en.wikipedia.org/wiki/Work_(physics);

"This calculation can be generalized for a constant force that is not directed along the line, followed by the particle. In this case the dot product F ⋅ ds = F cos θ ds, where θ is the angle between the force vector and the direction of movement.