The equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.
Let position vector of point P be:
p = 3 i + j + 2 k
Let position vector of point Q be:
q = i - 2 j - 4 k
So, PQ = Q - P
PQ = n = i - 2 j - 4 k - (3 i + j + 2 k)
n = i - 2 j - 4 k - 3 i - j - 2 k
n = - 2 i - 3 j - 6 k
The Equation of plane passing through point Q and perpendicular to PQ will be:
(r - q).n = 0
r n = q n
q n = (i - 2 j - 4 k) . (- 2 i - 3 j - 6 k)
q n = - 2 + 6 + 24
q n = 28
r n = 28
r (- 2 i - 3 j - 6 k) = 28
r (2 i + 3 j + 6 k) + 28 = 0
Therefore the equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.
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