What is the projection of #(-i + j + k)# onto # ( i -2j + 3k)#?

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Answer 1 · 2017-07-29T06:17:26

No projection since the vectors are perpendicular.

Let #vecb= <-1,1,1># and #veca= <1,-2,3>#

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

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

The dot product is

#veca.vecb=<-1,1,1> . <1,-2,3> =(-1*1)+(1*-2)+(1*3)#

#=-1-2+3=0#

The vectors #veca# and #vecb# are perpendicular.

So there is no projection posiible.