Question

If the vectors $PQ=-3i+4j+4k$ and $PR=5i-2j+4k$ are the sides of a $△PQR$, then the length of the median through $P$ is

• A. $\sqrt{14}$
• B. $\sqrt{15}$
• C. $\sqrt{17}$
• D. $\sqrt{18}$
• E. $\sqrt{19}$

Answer 1

The correct option is D $\sqrt{18}$

Given, $PQ=-3i+4j+4k$
and $PR=5i-2j+4k$
Therefore, the length of the median through $P$
$=\frac{1}{2}|PQ+PR|$
$=\frac{1}{2}|2i+2j+8k|$
$=\frac{1}{2}\sqrt{4+4+64}+\frac{1}{2}\sqrt{72}=\sqrt{18}$