Mathematics COMPONENTS OF A VECTOR ALONG AND PERPENDICULAR TO ANOTHER VECTOR
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COMPONENTS OF A VECTOR ALONG AND PERPENDICULAR TO ANOTHER VECTOR

Projection of vector

`text(Geometrical Interpretation :)`

Geometrically, the scalar product of two vectors is equal to the product of the magnitude of one and the projection of second in the direction of first vector i.e.

`vec(a)*vec(b)=|vec(a)| ` `(|vec(b)| cos theta)= |vec(a)| ` (projection of `vec(b)` in the direction of `vec(a)`)

Similarly `vec(a)*vec(b)= |vec(b)|` `( |vec(a)| cos theta)= |b| ` (projection of `vec(a)` in the direction of `vec(b)`)

Here projection of `vec(b)` on `vec(a)` = `(vec(a)*vec(b))/(| vec(a)|)`

Projection of `vec(a)` on `vec(b)` `= (vec(a)*vec(b))/(|vec(b)|)`

Components of `vec(b)` along & perpendicular to `vec(a)` :

`1.` Components of `vec(b)` along `vec(a)` = `vec(OM)`

`quadquadquadquadquad= OM hat(a) = ( b cos theta )hat(a)`

`quadquadquadquadquad= ((ab cos theta)/a ) hat(a) = (vec(a)*vec(b))/a^2 vec(a)`

`quadquadquadquadquad= ( (vec(a)*vec(b))/ |a|^2 )veca`

`2.` Component perpendicular to `vec(a)` =`vec(ON)`

`quadquadquadquadquad:.` `vec(ON) = vec(b)- vec(OM)`

`quadquadquadquadquadvec(ON) =vec(b) -( (vec(a)*vec(b))/a^2 )veca`
 
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