A) \[\sqrt{3}\]units
B) \[2\sqrt{5}\]units
C) 5 units
D) 10 units
Correct Answer: C
Solution :
Given, vector \[\overrightarrow{AB}=3\hat{i}+5\hat{j}+4\hat{k}\] and vector \[\overrightarrow{AC}=5\hat{i}-5\hat{j}+2\hat{k}\] Let AM is the median passing through the point A. \[\therefore \] \[\overrightarrow{AM}=\frac{1}{2}(\overrightarrow{AB}+\overrightarrow{AC})\] \[=\frac{1}{2}[(3\hat{i}+5\hat{j}+4\hat{k})+(5\hat{i}-5\hat{j}+2\hat{k})]\] \[=\frac{1}{2}[8\hat{i}+6\hat{k}]\] \[=4\hat{i}+3\hat{k}\] Length of median \[AM=\sqrt{{{4}^{2}}+{{3}^{2}}}\] \[=\sqrt{16+9}=\sqrt{25}=5\]unitsYou need to login to perform this action.
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