question_answer

The 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 triangle ABC. The length of the median through A is

A) \[\sqrt{288}\]               

B) \[\sqrt{72}\]                 

C) \[\sqrt{33}\]   

D) \[\sqrt{18}\]

Correct Answer: C

Solution :

[c] P. V. of M is \[(4,-1,4)\] Now, \[\overrightarrow{AM}=4\hat{i}-\hat{j}+4\hat{k}\] \[\therefore \,\,\,\,\left| \overrightarrow{AM} \right|=\sqrt{33}\]