Short Answer Type
The equation of plane through P (1, 2, –3) is
a (x – 1) + b (y – 2) +c (z +3) = 0 ...(1)
The direction ratios of the line through the points O (0, 0, 0) and P (1, 2, –3) are 1 - 0, 2 - 0, - 3 - 0.
i.e. ,1, 2,–3
∴ the line OP with direction ratios 1, 2, –3 is normal to the plane (1)
∴ equation (1) of plane becomes
1(x – 1) + 2 (y – 2) – 3 (z + 3) = 0
or x – 1 + 2y – 4-3z – 9 = 0 or x + 2y – 3z – 14 = 0.
and perpendicular to the vector 
.
Find the equation of a plane which passes through (2, –3, 1) and is perpendicular to the line through the points (3, 4, –1) and (2,–1, 5).
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