Q. 18

# 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, 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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