What is the projection of <2,-4,3 > onto <1,2,2 >?

1 Answer
Cosmic Defect
Feb 28, 2016

\vec{A_{}} id perpendicular to \vec{B_{}. So one's projection on the other must be a null vector ( <0,0,0>)

Explanation:

The projection of a \vec{A_{}} onto another vector \vec{B_{}} is:

\vec{A_B} = \frac{\vec{A_{}}.\vec{B_{}}}{B}\hat{B}=\frac{\vec{A_{}}.\vec{B_{}}}{B^2}\vec{B_{}}

Solution: \vec{A_{}}=<2,-4,3>; \qquad \vec{B_{}}=<1,2,2>;

\vec{A_{}}.\vec{B_{}}=(2\times1-4\times2+3\times2)=0

Since \vec{A_{}}.\vec{B_{}} = 0, it is clear that \vec{A_{}} is perpendicular to \vec{B_{}}. So its projection on \vec{B_{}} is a null vector.

Related questions
See all questions in Vector Operations
Impact of this question
1283 views around the world
You can reuse this answer
Creative Commons License