State True or False for the statements

If the foot of perpendicular drawn from the origin to a plane is (5, – 3, – 2),then the equation of plane is.






False


Let O be the origin, and P be the foot of the perpendicular drawn from the origin to plane


Then, position vector OP will be [which is normal of plane]



Unit vector of n is




Also,


By distance formula, we have distance between two points


A(x1, y1, z1) and B(x2, y2, z2) is





= √38


Now, equation of plane with unit normal vector and having perpendicular distance from origin d is



Equation of given plane is,




Which is given, hence statement is true!


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