​ Let P be a plane passing through the points (1, 0, 1), (1, –2, 1) and (0, 1, -2). Let a vector a = αi+βj+γk be such that vector a

Question

Let P be a plane passing through the points (1, 0, 1), (1, –2, 1) and (0, 1, -2). Let a vector \(\overset{\rightarrow}{a}=\alpha\hat i+\beta\hat j+\gamma\hat k\) be such that \(\overset{\rightarrow}{a}\) is parallel to the plane P, perpendicular to \((\hat i+2\hat j+3\hat k)\) and \(\overset{\rightarrow}{a}.(\hat i+\hat j+2\hat k)\) = 2, then (α - β+γ)² equals _______.

Answer 1

Answer is: 81

Equation of plane: