Question

The position vectors of the vertices of a triangles are $3\overline{i}+4\overline{j}+5\overline{k},\overline{i}+7\overline{k}$ and $5\overline{i}+5\overline{j}$. The distance between the circumcentre and orthocentre is

• A. $0$
• B. $\sqrt{306}$
• C. $2\sqrt{306}$
• D. $\frac{3}{2}\sqrt{306}$

Answer 1

Answer: (A)

$0$

Let $\overrightarrow{a}=3\hat{i}+4\hat{j}+5\hat{k}⟹a=5\sqrt{2}$

$\overrightarrow{b}=\hat{i}+7\hat{k}⟹b=5\sqrt{2}$

$\overrightarrow{c}=5\hat{i}+5\hat{j}⟹c=5\sqrt{2}$

$a=b=c⟹$ given triangle is equilateral triangle

In equilateral triangle ,circumcentre and orthocentre coincides

$⟹$ distance between circumcentre and orthocentre is $0$