If O be the origin and the coordinates of P be (1, 2, −3), then find the equation of the plane passing through P and perpendicular to OP.

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asked Jan 25, 2018 in Mathematics by sforrest072 (157,439 points) 61 410 949

If O be the origin and the coordinates of P be (1, 2, −3), then find the equation of the plane passing through P and perpendicular to OP.
 

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answered Jan 25, 2018 by mdsamim (213,225 points) 5 10 15
selected Jan 25, 2018 by sforrest072
 
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The coordinates of the points, O and P, are (0, 0, 0) and (1, 2, −3) respectively.
Therefore, the direction ratios of OP are (1 − 0) = 1, (2 − 0) = 2, and (−3 − 0) = −3
It is known that the equation of the plane passing through the point (x1, y1 z1) is

 where, a, b, and c are the direction ratios of normal. Here, the direction ratios of normal are 1, 2, and −3 and the point P is (1, 2, −3). Thus, the equation of the required plane is

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