question_answer

If vectors \[\overrightarrow{AB}=-3\hat{i}+4\hat{k}\] and \[\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\] are the sides of a \[\Delta \]ABC, then the length of the median through A is

A) \[\sqrt{14}\]      

B) \[\sqrt{18}\]

C) \[\sqrt{29}\]      

D) 5

Correct Answer: B

Solution :

[b] \[\overrightarrow{AB}+\overrightarrow{AC}=2\overrightarrow{AD}\] \[\therefore \overrightarrow{AD}=\frac{1}{2}\{(-3\hat{i}+4\hat{k})+(5\hat{i}-2\hat{j}+4\hat{k})\}\] \[=\hat{i}-\hat{j}+4\hat{k}\] Length of \[AD=\sqrt{1+1+16}=\sqrt{18}\]