Q. 18

Find the value of λ such that the line is perpendicular to the plane 3x - y – 2z = 7.

Answer :

Given :


Equation of line :


Equation of plane : 3x – y – 2z = 7


To Find :


Formulae :


1) Parallel vector to the line :


If equation of the line is then,


Vector parallel to the line is given by,



2) Normal vector to the plane :


If equation of the plane is ax + by + cz = d then,


Vector normal to the plane is given by,



3) Cross Product :


If are two vectors




then,



Answer :


For given equation of line,



Parallel vector to the line is



For given equation of plane,


3x – y – 2z = 7


normal vector to the plane is



As given line and plane are perpendicular to each other.





Comparing coefficients of on both sides



3λ = -6


λ = -2


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