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Answer 1 · 2017-03-30T14:25:14

The vector projection is $=<2/9,4/9,4/9>$
The scalar projection is $=2/3$

The vector projection of $veca$ over $vecb$ is

$=(veca.vecb)/(||vecb||)^2*vecb$

$vecb=<1,2,2>$

$veca=<2,-1,1>$

The dot product is

$veca.vecb=<2,-1,1>.<1,2,2>=2-2+2=2$

The modulus of $vecb$ is

$=||<1,2,2>||=sqrt(1+4+4)=sqrt9=3$

The vector projection is

$=2/9*<1,2,2>$

The scalar projection is

$=(veca.vecb)/||vecb||$

$=2/3$