Mathematics | VITEEE 2018 | Discussion Page

A unit vectorperpendicular to the plane formed by the points (1, 0, 1), (0,2,2) and (3, 3, 0) is

$\frac{1}{5\sqrt{3}}(5\hat{i}-\hat{j}-7\hat{k})$

$\frac{1}{5\sqrt{3}}(5\hat{i}-\hat{j}+7\hat{k})$

$\frac{1}{5\sqrt{3}}(5\hat{i}+\hat{j}+7\hat{k})$

D) None of these

Option B

Let A(1, 0, 1), B(0, 2,2) andc (3, 3, 0) be the given points, then

$\vec{AB}=-\hat{i}+2\hat{j}+2\hat{k}$ , $\vec{BC}=3\hat{i}+\hat{j}-2\hat{k}$

$\vec{AB}\times\vec{BC}=\begin{vmatrix}\hat{i} & \hat{j} & \hat{k} \\-1 & 2 & 1 \\ 3 & 1 & -2\end{vmatrix}= -5\hat{i}+\hat{j}-7\hat{k}$

.'. unit vector $\perp$ to the Plane: ABC

= $\pm\frac{1}{5\sqrt{3}}(-5\hat{i}+\hat{j}-7\hat{k})$

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