Q. 165.0( 1 Vote )

# If the line drawn from (4, -1, 2) meets a plane at right angles at the point (-10,5,4), find the equation of the plane.

It means the plane passes through the point B (-10, 5, 4). Therefore the position vector of this point is, And also given the line segment joining points A(4, -1, 2) and B (-10, 5, 4) and is at right angle to it.

Then  Position vector of - position vector of   We know that vector equation of a plane passing through point and perpendicular/normal to the vector is given by Substituting the values from eqn(i) and eqn(ii) in the above equation, we get   (by multiplying the two vectors using the formula )   is the vector equation of a required plane.

Let Then, the above vector equation of the plane becomes, Now multiplying the two vectors using the formula , we get  This is the Cartesian form of the equation of the required plane.

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