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