Let a = [ 1 , 2 , 3 ] {\displaystyle {\mathbf {a}}=[1,2,3]} , b = [ 1 , 1 , 1 ] {\displaystyle {\mathbf {b}}=[1,1,1]} and c = [ 1 , − 4 , 1 ] {\displaystyle {\mathbf {c}}=[1,-4,1]} . Find the projection of a {\displaystyle {\mathbf {a}}} onto b + c {\displaystyle {\mathbf {b}}+{\mathbf {c}}} .
![{\displaystyle {\mathbf {a}}=[1,2,3]}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/d7d9d875237ac94b9aac29ad081315de57d0328d)
, ![{\displaystyle {\mathbf {b}}=[1,1,1]}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/2658f9de409ec1eddcf211a08a7cc913f21932e5)
and ![{\displaystyle {\mathbf {c}}=[1,-4,1]}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/a728d3f8d4e2b32eae9941630eab090f65c38c9a)
. Find the projection of 
onto 
.
