What is the projection of (3i - j - 2k) onto (3i – 4j + 4k)?

1 Answer
Jan 16, 2018

The projection is =5/41<3, -4,4>

Explanation:

The vector projection of vecb onto veca is

proj_(veca)vecb=(veca.vecb)/(||veca||)^2veca

veca=<3,-4,4>

vecb= <3, -1,-2>

The dot product is

veca.vecb =<3,-4,4>. <3,-1,-2>

= (3)*(3)+(-4) *(-1)+(4)*(-2)=9+4-8=5

The modulus of veca is

=||veca||=||<3,-4,4>|| =sqrt((3)^2+(-4)^2+(4)^2)=sqrt41

Therefore,

proj_(veca)vecb=5/41<3, -4,4>