Question #0b785

1 Answer
Apr 14, 2017

Answer:

The vector projection is #=13/97<7,-8,-9>#
The scalar projection is #=26/sqrt194#

Explanation:

The vector projection of #vecA# over #vecB# is

#=(vecA.vecB)/(||vecB||^2)vecB#

#vecA=<2,-6,4>#

#vecB=<7,-8,-9>#

The dot product is

#vecA.vecB=<2,-6,4>.<7,-8,-9> =(2*7+6*8-9*4)=14+48-36=26#

The modulus of #vecB# is

#=||vecB||=||<7,-8,-9>||=sqrt(7^2+8^2+9^2)=sqrt194#

The vector projection is

#=26/194<7,-8,-9>#

The scalar projection is

#=(vecA.vecB)/(||vecB||)=26/sqrt194#