A) \[\sqrt{13}\]units
B) \[2\sqrt{5}\] units
C) 5 units
D) 10 units
Correct Answer: C
Solution :
[c] Let the given vectors be \[\overrightarrow{AB}=3\hat{i}+5\hat{j}+4\hat{k}\] and \[\overrightarrow{AC}=5\hat{i}-5\hat{j}+2\hat{k}\] Let AM be the median through A \[\therefore \overrightarrow{AM}=\frac{1}{2}(\overrightarrow{AB}+\overrightarrow{AC})\] \[=\frac{1}{2}[(3\hat{i}+5\hat{j}+4\hat{k})+(5\hat{i}-5\hat{j}+2\hat{k})]\] \[=\frac{1}{2}(8\hat{i}+6\hat{k})=(4\hat{i}+3\hat{k})\] \[\therefore \] Length of the median \[AM=\sqrt{{{4}^{2}}+{{3}^{2}}}\] \[=5\,units\]You need to login to perform this action.
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