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

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