Its Cartesian form will be 2x−y+z=b ...(i) ∵R is the mid-point of PQ. ∴R≡
P+Q
2
⇒R≡(−1,4,
a+2
2
) ∵R lies on the plane (i).
∴−2−4+
a+2
2
=b⇒a+2=2b+12
⇒a=2b+10...(ii) ∵ Direction ratio's of QP is (1−(−3),3−5,a−2) i.e. (4,−2,a−2) and direction ratios of normal to the given plane are (2,−1,1) ∵n and QP are parallel.
2
4
=
−1
−2
=
1
a−2
∴a−2=2⇒a=4 From Eq. (ii), b=−3 ∴|a+b|=|4−3|=|1|=1