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let's are the requested vector
r = ai + bj + ck
now given that
r and you are prependicular
therefore
r ,q is = 9
(ai+ bj +ck ). (i–2j+k)=0
a*1+b*(–2)+cx1=0
a–2b+c=0........(1)
also given that
r is coplanar with the vector p and q
therefore
P Q R =0
finding P q r
PQR = 1 1 1
1 –2 1
a b c
=1 [–2c–b]–1[c–a]+1[b+2a]
= –2c –b–c + a+ b + 2a
–3c+3a
this answer is right
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