The components of a vector `veca` along and perpendicular to a non-zero vector `vecb` are ________ and ___________, respectively.

Answer

`((veca.vecb)/(|vecb|^(2)))vecband veca-((veca.vecb)/|vecb|^(2))`

Explanation

Component of `veca` along `vecb`
`vec(OD) = OA cos theta.vecb/(|vecb|) `
`= ((veca.vecb)/(|vecb|))vecb/(|vecb|)= ((veca.vecb)/(|vecb|^(2)))vecb`
Component of `veca` perpendicular to `vecb`
`vec(DA) = veca - vec(OD)`
`= veca- (veca.vecb)/ (|vecb|^(2))vecb`