State True or False for the statements

The linelies in the plane

False

Given,

Equation of line,

Any point on this line should satisfy the plane equation to be on that plane,

Also any point of this line will have a position vector

Now, Given equation of plane

Putting a, in the above equation

= (2 + λ)(3) + (-3 – λ)(1) + (-1 + 2λ)(-1) + 2

= 6 – 3λ – 3 - λ + 1 – 2λ + 2

= 5 – 6λ ≠ RHS

Hence, Line doesn’t lies in the given plane