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.
Answer :
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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