Question

The vertices of a triangle ABC are (4, 2, 3); (1, 3, 1) and (-5, 5, -2) respectively. Find the length of the perpendicular drawn from origin O to plane of $\Delta ABC.$

• A. $\sqrt{7}$
• B. $\sqrt{10}$
• C. $\sqrt{12}$
• D. $\sqrt{15}$

Answer 1

The correct option is B $\sqrt{10}$

Normal to plane $ABC$ is $n=\overrightarrow{AB}\times \overrightarrow{AC}=i+3j$
$p=$ projection of $\overrightarrow{OA}$ on $n=\frac{\overrightarrow{OA.n}}{\left|n\right|}=\sqrt{10}$