Question

lf $A=(-3,2,5),B=(-3,4,5)$ and $C=(-3,4,7)$ are the position vectors of vertices of $\Delta ABC$ then its circumcentre is

• A. $(-3,3,5)$
• B. $(-3,3,6)$
• C. $(-3,4,6)$
• D. $(-3,4,7)$

Answer 1

The correct option is B $(-3,3,6)$

$\overrightarrow{AB}=2\hat{j}$

$\overrightarrow{AC}=2\hat{j}+2\hat{k}$

$\overrightarrow{BC}=2\hat{k}$
Triangle $ABC$ is right angled at angle $B$.
Hence, the circumcentre is mid point of $AC$. Let the circumcentre be $D$.
$=\frac{1}{2}(-6,6,12)$
$=(-3,3,6)$