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# If $\overrightarrow {AB}=3\hat i+\hat j-2\hat k,\:and \:\overrightarrow {AC}=-\hat i+3\hat j+4\hat k$ are two sides af the $\Delta ABC$, then the length of the median through $A$ is ?

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$\overrightarrow {BC}=\overrightarrow {AC}-\overrightarrow {AB}=-4\hat i+2\hat j+6\hat k$
Median through $A$ = $\large\frac{\overrightarrow {AC}-\overrightarrow {AB}}{2}$$=-2\hat i+\hat j+3\hat k$
Length pf median $= \sqrt {4+1+9}=\sqrt {14}$

answered Dec 1, 2013
edited Dec 1, 2013