How do you determine whether u and v are orthogonal, parallel or neither given #u=i# and #v=-2i+2j#?

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Answer 1 · 2016-11-23T14:07:27

#vecu,vecv# neither parallel nor orthogonal

1) Checking parallel property.

for parallel vectors

#veca=lambdavecb##" "#for some#" "lambda#

#vecu=veci#

#vecv=-2veci+2vecj#

in this case, since #"vecu# has no #vecj" "#component

#vecu!=lambdavecv#

2) Checking for orthogonal ( perpendicular )property.

for #vecu_|_vecv," "vecu.vecv=0#

#vecu.vecv=veci.(-2veci+2vecj)#

for vectors:#" veci.veci=1, " "veci.vecj=0#

So

#vecu.vecv=-2veci.veci+2veci.vecj#

#vecu.vecv=-2veci.veci+cancel(2veci.vecj)#

#vecu.vecv=-2#

#vecu.vecv!=0, cancel_|_#

#vecu,vecv# neither parallel nor orthogonal