What is the projection of #<6,-4,9 ># onto #<7,8,7 >#?

1 Answer
Feb 4, 2017

Answer:

The vector projection is #=73/162<7,8,7>#
The scalar projection #=73/sqrt162#

Explanation:

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

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

The dot product is

#veca.vecb=<7,8,7>.<6,-4,9>=42-32+63=73#

The modulus of #veca# is

#||veca||=||<7,8,7>||=sqrt(49+64+49)=sqrt162#

The vector projection is

#=73/162<7,8,7>#

The scalar projection is

#(veca.vecb)/(||veca||)=73/sqrt162#