What is the projection of #<7,-8,3 ># onto #<5,-6,1 >#?

1 Answer
Feb 19, 2017

Answer:

The vector projection is #=43/31<5,-6,1>#
The scalar projection is #=86/sqrt62#

Explanation:

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

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

The dot product is

#veca.vecb=<5,-6,1>*<7,-8,3>#

#=5*7+(-6*-8)+3*1#

#=35+48+3#

#=86#

The modulus of #veca# is

#||veca||=||<5,-6,1>||#

#=sqrt(25+36+1)#

#=sqrt62#

The vector projection is

#=86/62*<5,-6,1>#

#=43/31<5,-6,1>#

The scalar projection is

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

#=86/sqrt62#