What is the projection of #(j+2k)# onto # ( i+2j)#?

1 Answer
Dec 7, 2016

Answer:

Scalar projection is #2/sqrt5#

and vector projection is #2/5j+4/5k#

Explanation:

Projection of a vector #veca# onto another vector #vecb# could be scalar projection or vector projection.

A scalar projection is #(veca*vecb)/|veca|# and vector projection is #(veca*vecb)/(veca*veca)*veca#, where #veca# is one on whom we are seeking projection

Here as #vecb=(i+2j)# and #veca=(j+2k)#, hence

#veca*vecb=1xx0+2xx1+0xx2=2#

and #veca*veca=1xx1+2xx2=5# and hence #|veca|=sqrt5#

Hence scalar projection is #2/sqrt5#

and vector projection is #2/5xx(j+2k)=2/5j+4/5k#