​ A plane passes through the points A(1, 2, 3), B(2, 3, 1) and C(2, 4, 2). If vector(OP) is the origin and P is (2, -1, 1),

Question

A plane passes through the points A(1, 2, 3), B(2, 3, 1) and C(2, 4, 2). If O is the origin and P is (2, -1, 1), then the projection of \(\overrightarrow{OP}\) on this plane is of length :

(1) \(\sqrt{\frac 27}\)

(2) \(\sqrt{\frac 23}\)

(3) \(\sqrt{\frac {2}{11}}\)

(4) \(\sqrt{\frac 25}\)

Answer 1

Correct Option is (3) \(\sqrt{\frac 23}\)

Normal to plane \(\vec n=\begin{vmatrix} \vec i & \vec j & \vec k \\ 1 & 1 & -2 \\ 0 & 1 & 1 \end{vmatrix}\)