How do you find the angle between the vectors #v=i+2j, w=2i-j#?

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Answer 1 · 2017-10-21T13:48:09

#90^0#

we `will use the scalar (dot) product

#veca*vecb=|veca||vecb|costheta--(1)#

where #theta# is the angle between the vectors

we are given

#vecv=veci+2vecj, vecw=2veci-vecj#

now if we have two vectors in component form

#veca=a_xveci+a_yvecj, vecb=b_xveci+b_yvecj#

then #veca*vecb=a_xbx+a_yb_y#

so in this question

#vecv.vecw=(veci+2vecj)*( 2veci-vecj)#

#veca*vecb=1xx2+2xx -1#

#veca*vecb=2-2=0#

so the dot product #=0#

from #(1)# this implies that

#costheta=0=>theta=90^0#

so the vectors are at right angles to each other