# Decomposition of a vector.

Decompose 6i-3j-6k into vectors parallel and perpendicular to following vectors.

a) i+j+k

b) 2i-j-2k

c) 2j-k

https://brainmass.com/math/vector-calculus/decomposition-vector-340060

#### Solution Preview

The standard procedure for representing a vector V as a sum of two vectors V_1 and V_2, one parallel to the given one and one perpendicular to the given vector W (thus, decomposing V) is to find the orthogonal projection Proj_W (V) of V onto W (and this will be the vector parallel to W) and then subtract this projection from the original vector V, thus obtaining the perpendicular vector. More ...

#### Solution Summary

The process of decomposing a vector into the sum of components perpendicular and parallel to another vector is examined and illustrated.

$2.19