What is the projection of (3i + 2j - 6k) onto (3i - j - 2k)?

1 Answer
Narad T.
Nov 2, 2016

The answer is =19/(7sqrt14)(3i-j-2k)

Explanation:

Let veca=〈3,-1,-2〉 and vecb=〈3,2,-6〉
Then the vector projection of vecb upon veca is
(veca.vecb)/(∥veca∥∥vecb∥)veca
The dot product veca.vecb=〈3,-1,-2〉.〈3,2,-6〉=9-2+12=19
The modulus ∥veca∥=sqrt(9+1+4)=sqrt14
The modulus ∥vecb∥=sqrt(9+4+36)=sqrt49=7
the projection is =19/(7sqrt14)〈3,-1,-2〉

Related questions
See all questions in Vector Operations
Impact of this question
1410 views around the world
You can reuse this answer
Creative Commons License