What is the projection of #<7,-5,6 ># onto #<-1,-3,7 >#?

1 Answer
Feb 13, 2017

Answer:

The vector projection is #=50/59<-1,-3,7>#
The scalar projection is #=50/sqrt59#

Explanation:

The vector projection of #vecb# onto #veca# is

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

The dot product is

#veca.vecb= <-1,-3,7>.<7,-5,6> =-7+15+42=50#

The modulus of #veca# is

#||<-1,-3,7>||=sqrt(1+9+49)=sqrt59#

The vector projection is #=50/59<-1,-3,7>#

The scalar projection is #=(veca.vecb)/(||veca||)=50/sqrt59#