Three Dimensional Geometry Part 2

Given equation of plane in vector form is r⋅(2

∧

i

−

∧

j

+

∧

k

)−b=0Its 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).
⇒‌‌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