Question
Show that the plane whose vector equation is 
contains the line whose vector equation is 
Solution
The equation of given plane is
...(1)
The equation of given plane is
...(2)
Now line (2) passes through the point (1, 1, 0) with position vector
and is parallel to the vector 
Now plane (1) passes through the point with position vector
if
i.e. if 1 + 2 -0 = 3
i.e. if 3 = 3, which is true
Now,
is a vector normal to the plane (1). It will be perpendicular to the line (2) if it is perpendicular to 
i.e. if
i.e. if 2 + 2 – 4 = 0
i.e. if 0 = 0, which is true
∴ plane (1) contains the line (2 )
...(1)The equation of given plane is
...(2)Now line (2) passes through the point (1, 1, 0) with position vector
and is parallel to the vector Now plane (1) passes through the point with position vector
if
i.e. if 1 + 2 -0 = 3
i.e. if 3 = 3, which is true
Now,
is a vector normal to the plane (1). It will be perpendicular to the line (2) if it is perpendicular to i.e. if
i.e. if 2 + 2 – 4 = 0
i.e. if 0 = 0, which is true
∴ plane (1) contains the line (2 )
