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

1 Answer
Shwetank Mauria
Dec 7, 2016

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

Related questions
See all questions in Vector Operations
Impact of this question
2008 views around the world
You can reuse this answer
Creative Commons License