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# The length of median through $A$ of the $\Delta\:ABC$ where $\overrightarrow {AB}=3\hat i+4\hat k\:\:and\:\:\overrightarrow {AC}=5\hat i-2\hat j+4\hat k$ is ?

$(a)\sqrt {72}\:\:\:\:\qquad\:\:(b)\:\:\sqrt { 33}\:\:\:\:\qquad\:\:(c)\:\:\sqrt {288}\:\:\:\:\qquad\:\:(d)\:\:\sqrt {18}$

Toolbox:
• Median through $A$ of a $\Delta \:ABC$ is $\large\frac{\overrightarrow {AB}+\overrightarrow {AC}}{2}$
Given : $\overrightarrow {AB}=3\hat i +4\hat k\:\:\:and\:\:\:\overrightarrow {AC}=5\hat i-2\hat j+4\hat k$
$\overrightarrow {AB}+\overrightarrow {AC}=8\hat i-2\hat j+8\hat k$
Median through $A$ of a $\Delta \:ABC$ is $\large\frac{\overrightarrow {AB}+\overrightarrow {AC}}{2}$
$=\large\frac{1}{2}$$(8\hat i-2\hat j+8\hat k)=4\hat i-\hat j+4\hat k$
$\therefore$ length of median = $\sqrt {16+1+16}=\sqrt {33}$
edited Mar 12, 2014