Vector Algebra Question 203
Question: 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
Options:
A) $ \sqrt{14} $
B) $ \sqrt{18} $
C) $ \sqrt{29} $
D) 5
Show Answer
Answer:
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} $
BETA
